[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/10213#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/10213","headline":"\u8907\u96d1\u306a\u5fae\u5206\u5f62\u5f0f-Wikipedia","name":"\u8907\u96d1\u306a\u5fae\u5206\u5f62\u5f0f-Wikipedia","description":"before-content-x4 \u4e00 \u8907\u96d1\u306a\u5fae\u5206\u5f62\u5f0f \u8907\u96d1\u306a\u30b8\u30aa\u30e1\u30c8\u30ea\u304b\u3089\u306e\u6570\u5b66\u7684\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3067\u3059\u3002\u8907\u96d1\u306a\u5fae\u5206\u5f62\u5f0f\u306f\u3001\u8907\u96d1\u306a\u591a\u69d8\u6027\u306b\u95a2\u3059\u308b\uff08\u5b9f\u969b\u306e\uff09\u5fae\u5206\u5f62\u5f0f\u306e\u5bfe\u5fdc\u3067\u3059\u3002\u5b9f\u969b\u306e\u5834\u5408\u3068\u540c\u69d8\u306b\u3001\u8907\u96d1\u306a\u5fae\u5206\u5f62\u614b\u306f\u5927\u5b66\u9662\u4ee3\u6570\u3082\u5f62\u6210\u3057\u307e\u3059\u3002\u7a0b\u5ea6\u304b\u3089\u306e\u8907\u96d1\u306a\u5fae\u5206\u5f62\u5f0f k {displaystyle k} after-content-x4 \uff08\u307e\u305f\u306f\u7565\u3057\u3066K\u5b57\u578b\uff09\u306f\u3001\u660e\u78ba\u306a\u65b9\u6cd5\u30672\u3064\u306e\u5fae\u5206\u5f62\u5f0f\u306b\u5206\u89e3\u3067\u304d\u307e\u3059\u3002 p {displaystyle p} \u307e\u305f Q {displaystyle q} \u3068 after-content-x4 p +","datePublished":"2023-03-03","dateModified":"2023-03-03","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/c3c9a2c7b599b37105512c5d570edc034056dd40","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/c3c9a2c7b599b37105512c5d570edc034056dd40","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/10213","wordCount":10802,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u4e00 \u8907\u96d1\u306a\u5fae\u5206\u5f62\u5f0f \u8907\u96d1\u306a\u30b8\u30aa\u30e1\u30c8\u30ea\u304b\u3089\u306e\u6570\u5b66\u7684\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3067\u3059\u3002\u8907\u96d1\u306a\u5fae\u5206\u5f62\u5f0f\u306f\u3001\u8907\u96d1\u306a\u591a\u69d8\u6027\u306b\u95a2\u3059\u308b\uff08\u5b9f\u969b\u306e\uff09\u5fae\u5206\u5f62\u5f0f\u306e\u5bfe\u5fdc\u3067\u3059\u3002\u5b9f\u969b\u306e\u5834\u5408\u3068\u540c\u69d8\u306b\u3001\u8907\u96d1\u306a\u5fae\u5206\u5f62\u614b\u306f\u5927\u5b66\u9662\u4ee3\u6570\u3082\u5f62\u6210\u3057\u307e\u3059\u3002\u7a0b\u5ea6\u304b\u3089\u306e\u8907\u96d1\u306a\u5fae\u5206\u5f62\u5f0f k {displaystyle k}        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\uff08\u307e\u305f\u306f\u7565\u3057\u3066K\u5b57\u578b\uff09\u306f\u3001\u660e\u78ba\u306a\u65b9\u6cd5\u30672\u3064\u306e\u5fae\u5206\u5f62\u5f0f\u306b\u5206\u89e3\u3067\u304d\u307e\u3059\u3002 p {displaystyle p} \u307e\u305f Q {displaystyle q} \u3068        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4p + Q = k {displaystyle p+q = k} \u3082\u3064\u3002\u3053\u306e\u5206\u89e3\u3092\u5f37\u8abf\u3059\u308b\u305f\u3081\u306b\u3001 \uff08P\u3001Q\uff09-Form \u3002\u307e\u305f\u3001\u3053\u306e\u77ed\u3044\u30b9\u30d4\u30fc\u30c1\u306f\u3001\u5b9f\u969b\u306e\u30d5\u30a9\u30fc\u30e0\u306b\u306f\u305d\u306e\u3088\u3046\u306a\u89e3\u4f53\u304c\u306a\u3044\u305f\u3081\u3001\u305d\u308c\u3089\u304c\u8907\u96d1\u306a\u5fae\u5206\u5f62\u614b\u3067\u3042\u308b\u3053\u3068\u3092\u660e\u78ba\u306b\u3057\u307e\u3059\u3002\u8907\u96d1\u306a\u5fae\u5206\u5f62\u5f0f\u306e\u8a08\u7b97\u306f\u3001\u30db\u30c3\u30b8\u7406\u8ad6\u306b\u304a\u3044\u3066\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002 \u591a\u5206 m {displaystyle m} \uff08\u8907\u96d1\u306a\uff09\u6b21\u5143\u306e\u8907\u96d1\u306a\u591a\u69d8\u6027 n {displaystyle n} \u3002\u9078\u3076        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4{ dzj= d xj+ \u79c1 d yj\u3001  dz\u00afj= d xj –  \u79c1 d yj;  \u521d\u3081 \u2264 j \u2264 n } {displaystyle {mathrm {d} z^{j} = dx^{j}+idy^{j}\u3001mathrm {d} {bar {z}}^{j} = dx^{j} -idy^j}; 1leq jleq n}} \u8907\u96d1\u306a\u4ef2\u9593\u306e\u30a2\u30fc\u30c6\u30a3\u30b9\u30c8\u306e\u5730\u5143\u306e\u57fa\u76e4\u3068\u3057\u3066\u3002\u5171\u30d9\u30af\u30bf\u30fc\u306b\u306f\u30ed\u30fc\u30ab\u30eb\u8868\u73fe\u304c\u3042\u308a\u307e\u3059 \u2211j=1nfjdzj+ gjdz\u00afj\u3002 {displaystyle sum _ {j = 1}^{n} f_ {j} mathrm {d} z {j}+g_ {j} mathrm {d} {overline {z}}^{j}\u3002}\u3002 \u30d5\u30a9\u30fc\u30e0\u306e\u57fa\u672c\u7684\u306a\u30d9\u30af\u30c8\u30eb\u306e\u307f\u304c dzj{displaystyle\u30c6\u30ad\u30b9\u30c8\u30b9\u30bf\u30a4\u30ebMathrm {d} z^{j}} \u767a\u751f\u306f\u53e3\u982d\u3067\uff081.0\uff09\u5f62\u5f0f\u3067\u3042\u308a\u3001\u30d5\u30a9\u30fc\u30df\u30e5\u30e9\u30d9\u30fc\u30b9 A1,0\uff08 m \uff09\uff09 {displaystyle {mathcal {a}}^{1,0}\uff08m\uff09} \u5c02\u7528\u3002\u3053\u308c\u306b\u985e\u4f3c\u3057\u3066\u3044\u307e\u3059 A0,1\uff08 m \uff09\uff09 {displaystyle {mathcal {a}}^{0,1}\uff08m\uff09} \uff080.1\uff09\u30d5\u30a9\u30fc\u30e0\u306e\u7a7a\u9593\u3001\u3059\u306a\u308f\u3061\u3001\u5f62\u5f0f\u306e\u57fa\u672c\u7684\u306a\u30d9\u30af\u30c8\u30eb\u306e\u307f dz\u00afj{displaystyle Text Style Mathrm {d} {overline {z}^{j}} \u3082\u3064\u3002\u3053\u308c\u3089\u306e2\u3064\u306e\u90e8\u5c4b\u306f\u5b89\u5b9a\u3057\u3066\u3044\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u30db\u30ed\u30e2\u30fc\u30d5\u30a3\u30c3\u30af\u5ea7\u6a19\u306e\u5909\u66f4\u306e\u4e0b\u3067\u3001\u3053\u308c\u3089\u306e\u90e8\u5c4b\u306f\u305d\u308c\u81ea\u4f53\u3067\u8868\u793a\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u305f\u3081\u3001\u90e8\u5c4b\u306f\u305d\u3046\u3067\u3059 A1,0\uff08 m \uff09\uff09 {displaystyle {mathcal {a}}^{1,0}\uff08m\uff09} \u3068 A0,1\uff08 m \uff09\uff09 {displaystyle {mathcal {a}}^{0,1}\uff08m\uff09} \u8907\u96d1\u306a\u30d9\u30af\u30c8\u30eb\u30d0\u30f3\u30c9\u30eb m {displaystyle m} \u3002 \u8907\u96d1\u306a\u5fae\u5206\u5f62\u5f0f\u306e\u5916\u90e8\u7a4d\u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u3001\u3053\u308c\u306f\u5b9f\u969b\u306e\u5fae\u5206\u5f62\u5f0f\u3068\u540c\u69d8\u306b\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3001\u4eca\u3067\u306f\u90e8\u5c4b\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002 \uff08 p \u3001 Q \uff09\uff09 {displaystyle\uff08p\u3001q\uff09}  – \u30d5\u30a9\u30fc\u30df\u30f3\u30b0\u30b9\u30eb\u30fc Ap,q\uff08 m \uff09\uff09 \uff1a= \u22c0j=1pA1,0\uff08 m \uff09\uff09 \u2227 \u22c0j=1qA0,1\uff08 m \uff09\uff09 {displaystyle {mathcal {a}}^{p\u3001q}\uff08m\uff09\uff1a= bigwedge _ {j = 1}^{p} {mathcal {a}}^{1,0}\uff08m\uff09\u30a6\u30a7\u30c3\u30b8bigwedge _ {j = 1}^{q} {Q} {a} {a} {a} {qune \u5b9a\u7fa9\u3002\u90e8\u5c4b\u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059 Er\uff08 m \uff09\uff09 {displaystyle {mathcal {e}}^{r}\uff08m\uff09} \u76f4\u63a5\u5408\u8a08\u3068\u3057\u3066 Er\uff08 m \uff09\uff09 \uff1a= \u2a01p+q=rAp,q\uff08 m \uff09\uff09 {displaystyle {mathcal {e}}^{r}\uff08m\uff09\uff1a= bigoplus _ {p+q = r} {mathcal {a}}^{p\u3001q}\uff08m\uff09}}  \uff08 p \u3001 Q \uff09\uff09 {displaystyle\uff08p\u3001q\uff09}  – \u3067\u30d5\u30a9\u30fc\u30e0 r = p + Q {displaystyle r = p+q} \u3002\u3053\u308c\u306f\u3001\u76f4\u63a5\u7684\u306a\u5408\u8a08\u306e\u7b49\u578b\u3067\u3059 Er\uff08 m \uff09\uff09 \u2245 Ar\uff08 m \uff09\uff09 \u2295 \u79c1 Ar\uff08 m \uff09\uff09 {displaystyle {mathcal {e}}^{r}\uff08m\uff09cong {mathcal {a}}^{r}\uff08m\uff09oplus i {mathcal {a}}^{r}\uff08m\uff09} \u672c\u5f53\u306e\u9055\u3044\u306e\u90e8\u5c4b\u3002\u307e\u305f\u3001\u305d\u306e\u305f\u3081\u3067\u3059 p + Q = r {displaystyle p+q = r} \u6295\u5f71 \u03c0p,q\uff1a Er\uff08 m \uff09\uff09 \u2192 Ap,q\uff08 m \uff09\uff09 {displaystyle pi _ {p\u3001q} colon {mathcal {e}}^{r}\uff08m\uff09\u304b\u3089{mathcal {a}}^{p\u3001q}\uff08m\uff09}} \u5404\u8907\u96d1\u306a\u5fae\u5206\u5f62\u5f0f\u306e\u3069\u308c\u304c\u7a0b\u5ea6\u304b\u3089\u5b9a\u7fa9\u3057\u307e\u3057\u305f\u304b r {displaystyle r} \u5f7c\u5973 \uff08 p \u3001 Q \uff09\uff09 {displaystyle\uff08p\u3001q\uff09}  – \u5272\u308a\u5f53\u3066\u3002 \u4e00 \uff08 p \u3001 Q \uff09\uff09 {displaystyle\uff08p\u3001q\uff09} \u3057\u305f\u304c\u3063\u3066\u3001-form\u306b\u306f\u30ed\u30fc\u30ab\u30eb\u5ea7\u6a19\u304c\u3042\u308a\u307e\u3059 \u3068 1\u3001 … \u3001 \u3068 n{displaystyle z_ {1}\u3001ldots\u3001z_ {n}} \u660e\u78ba\u306a\u8868\u73fe \u304a\u304a = \u22111\u2264j1q1\u2264i1pfi1,\u2026ip,j1,\u2026jqdzi1\u2227 \u22ef \u2227 dzip\u2227 dz\u00afj1\u2227 \u22ef \u2227 dz\u00afjq\u3002 {displaystyle omega = sum _ {stackrel {1leq i_ {1} dz\u00afJ\uff1a= \u22111\u2264j1q1\u2264i1pfi1,\u2026ip,j1,\u2026jqdzi1\u2227 \u22ef \u2227 dzip\u2227 dz\u00afj1\u2227 \u22ef \u2227 dz\u00afjq{displaystyle sum _ {i\u3001j} f_ {i\u3001j} mathrm {d} z_ {i}\u30a6\u30a7\u30c3\u30b8Mathrm {d} {overline {z}} _ {j}\uff1a= sum _ {stackrel {1leq i_ {1}} p+q=rAp,q\uff08 m \uff09\uff09 \u2192 \u2a01p+q=rAp+1,q\uff08 m \uff09\uff09 \u2295 \u2a01p+q=rAp,q+1\uff08 m \uff09\uff09 \u3001 {disdisplaystyle mathrm {d}\uff1abigopoplus _ {p+q = r} {mathcal {}}^{p\u3001q}\uff08m\uff09\u304b\u3089bigopoplus _ {p+q = r} {mathcal {{p+1\u3001q}} \u5165\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059 d = \u2202 + \u2202\u00af{displaystyle mathrm {d} = partial +{overline {partial}}}} \u5206\u5272\u3059\u308b\u3002 Dolbeuult\u30aa\u30da\u30ec\u30fc\u30bf\u30fc \u2202 \uff1a Ap,q\uff08 m \uff09\uff09 \u2192 Ap+1,q\uff08 m \uff09\uff09 {displaystyle partial\uff1a{mathcal {a}}^{p\u3001q}\uff08m\uff09\u304b\u3089{mathcal {a}}^{p+1\u3001q}\uff08m\uff09} \u3068 \u2202\u00af\uff1a Ap,q\uff08 m \uff09\uff09 \u2192 Ap,q+1\uff08 m \uff09\uff09 {displaystyle {overline {partial}}\uff1a{mathcal {a}}^{p\u3001q}\uff08m\uff09to {mathcal {a}}^{p\u3001q+1}\uff08m\uff09}}} \u3067\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059 \u2202:=\u03c0p+1,q\u2218d\u2202\u00af:=\u03c0p,q+1\u2218d.{displayStyle {begin {aligned} partial\uff06\uff1a= pi _ {p+1\u3001q} circ mathrm {d} \\ {overial} {partial}}\uff06\uff1a= pi _ {p\u3001q+1} circ mathrm {d} .end}}}}} \u30ed\u30fc\u30ab\u30eb\u5ea7\u6a19\u3067\u306f\u3001\u3053\u308c\u306f\u610f\u5473\u304c\u3042\u308a\u307e\u3059 \u2202 (\u2211I,JfI,JdzI\u2227dz\u00afJ)= \u2211I,J\u2211l=1n\u2202fI,J\u2202zldzl\u2227 dzI\u2227 dz\u00afJ{displaystyle partial Left\uff08sum _ {i\u3001j} f_ {i\u3001j} mathrm {d} z^{i}\u30a6\u30a7\u30c3\u30b8Mathrm {d} {overline {z}}^{j} right\uff09= sum _ {i\u3001j} sum _ {l} {n} {n} {fra z^{l}}} mathrm {d} z^{l} wedge mathrm {d} z^{i}\u30a6\u30a7\u30c3\u30b8Mathrm {d} {overline {z}}^{j}}}} \u3068 \u2202\u00af(\u2211I,JfI,JdzI\u2227dz\u00afJ)= \u2211I,J\u2211l=1n\u2202fI,J\u2202z\u00afldz\u00afl\u2227 dzI\u2227 dz\u00afJ\u3002 {displayStyle {overline {partial}}\u5de6\uff08sum _ {i\u3001j} f_ {i\u3001j} mathrm {d} z^{i}\u30a6\u30a7\u30c3\u30b8Mathrm {d} {overline {z}}}^{j} right\uff09= sum _ {n {i {l = 1} {l = 1} {n {n} \u3001j}} {partial {overline {z}}^{l}}} mathrm {d} {overline {z}}^{l}\u30a6\u30a7\u30c3\u30b8Mathrm {d} {i}\u30a6\u30a7\u30c3\u30b8Mathrm {d} {andline \u3042\u308b \u2202 {displaystyle partial} \u3068 \u2202\u00af{displaystyle {overline {partial}}} \u65b9\u7a0b\u5f0f\u306e\u53f3\u5074\u306b\u3042\u308b\u901a\u5e38\u306e\u30c9\u30eb\u30d9\u30a4\u6f14\u7b97\u5b50\u3002 Holomorphe Diffirfialformen [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5fae\u5206\u5f62\u5f0f\u3092\u6e80\u305f\u3057\u307e\u3059 \u304a\u304a \u2208 Ap,0\uff08 m \uff09\uff09 {displaystyle omega in {mathcal {a}}^{p\u30010}\uff08m\uff09} \u65b9\u7a0b\u5f0f \u2202\u00af\u304a\u304a = 0 {displaystyle {overline {partial}} omega = 0} \u3001\u305d\u306e\u305f\u3081\u3001\u30db\u30ed\u30e2\u30fc\u30d5\u30a3\u30c3\u30af\u306e\u5fae\u5206\u5f62\u614b\u306b\u3064\u3044\u3066\u8a71\u3057\u307e\u3059\u3002\u30ed\u30fc\u30ab\u30eb\u5ea7\u6a19\u3067\u306f\u3001\u3053\u308c\u3089\u306e\u30d5\u30a9\u30fc\u30e0\u3092\u901a\u904e\u3067\u304d\u307e\u3059 \u2211IfIdzI{displaystyle sum _ {i} f_ {i} mathrm {d} z^{i}} \u8868\u73fe\u3057\u307e\u3059 f I{displaystyle f_ {i}} \u30db\u30ed\u30e2\u30fc\u30d5\u306f\u95a2\u6570\u3067\u3059\u3002\u30db\u30ed\u30e2\u30eb\u30d5\u306e\u30d9\u30af\u30c8\u30eb\u30eb\u30fc\u30e0 p {displaystyle p} -ON m {displaystyle m} \u30a6\u30a3\u30eb \u304a\u304a p\uff08 m \uff09\uff09 {displaystyle omega ^{p}\uff08m\uff09} \u66f8\u304d\u7559\u3081\u305f\u3002 \u7279\u6027 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] Leibniz\u30eb\u30fc\u30eb\u304c\u3053\u308c\u3089\u306e\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u306b\u9069\u7528\u3055\u308c\u307e\u3059\u3002\u306a\u308c \u304a\u304a \u2208 Ap,q{displaystyle omega in {mathcal {a}}^{p\u3001q}} \u3068 n \u2208 Ar,s{displaystyle nu in {mathcal {a}}^{r\u3001s}} \u305d\u306e\u5f8c\u3001\u9069\u7528\u3055\u308c\u307e\u3059 \u2202(\u03c9\u2227\u03bd)=\u2202\u03c9\u2227\u03bd+(\u22121)p+q\u03c9\u2227\u2202\u03bd{displaystyle partial\uff08omega wedge nu\uff09= partial omega wedge nu +\uff08-1\uff09^{p +q}\u3001omega wedge partial nu} \u3068 \u2202\u00af(\u03c9\u2227\u03bd)=\u2202\u00af\u03c9\u2227\u03bd+(\u22121)p+q\u03c9\u2227\u2202\u00af\u03bd.{displaystyle {overline {partial}}\uff08omega wedge now\uff09= {overline {partial}} omega wcege now +\uff08-1\uff09^{p +q}\u3001omega wedge {partial}}}}} 0=d2=(\u2202+\u2202\u00af)2=\u22022+(\u2202\u00af\u2202+\u2202\u2202\u00af)+\u2202\u00af2{displaystyle 0 = mathrm {d} ^{2} =\uff08partial +{overline {partial}}\uff09 ^{2} = partial ^{2} +\uff08{overline {partial}} partial +partial {anuverline {artial}} \u7d9a\u304d\u307e\u3059 \u22022= 0 {displaystyle partial ^{2} = 0} \u3001 \u2202 \u2202\u00af+ \u2202\u00af\u2202 = 0 {displaystyle partial {overline {partial}}+{overline {partial}} partial = 0} \u3068 \u2202\u00af2= 0 {displaystyle {overline {partial}}^{2} = 0} \u30013\u3064\u306e\u7528\u8a9e\u306f\u3059\u3079\u3066\u7a0b\u5ea6\u304c\u7570\u306a\u308b\u305f\u3081\u3067\u3059\u3002\u30aa\u30da\u30ec\u30fc\u30bf\u30fc \u2202 {displaystyle partial} \u3068 \u2202\u00af{displaystyle {overline {partial}}} \u305d\u306e\u305f\u3081\u3001\u30b3\u30db\u30e2\u30ed\u30b8\u30fc\u7406\u8ad6\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306b\u306f\u3001Dolbault Coomology\u3068\u3044\u3046\u540d\u524d\u304c\u4ed8\u3044\u3066\u3044\u307e\u3059\u3002 \u591a\u5206 \uff08 m \u3001 g \uff09\uff09 {displaystyle\uff08m\u3001g\uff09} K\u00e4ttermannigfaltigkeit\u3001\u3059\u306a\u308f\u3061\u3001\u8a31\u5bb9\u3067\u304d\u308bRiemann Metrik\u306e\u8907\u96d1\u306a\u591a\u69d8\u6027 g {displaystyle g} \u3001Anduncatenials dlobealolt-cross-operator\u3068\u8a00\u3046\u4eba \u2202\u00af\u2217{displaystyle {overline {partial}}^{*}} \u3053\u306e\u30e1\u30c8\u30ea\u30c3\u30af\u306b\u95a2\u3057\u3066\u30d5\u30a9\u30fc\u30e0\u3002\u30aa\u30da\u30ec\u30fc\u30bf\u30fc d \uff1a= \u2202\u00af\u2202\u00af\u2217+ \u2202\u00af\u2217\u2202\u00af{displaystyle delta\uff1a= {overline {partial}}\u3001{overline {partial}}^{*}+{overline {partial}}^{*} {overline {partial}}}}} \u6b21\u306b\u3001\u4e00\u822c\u5316\u3055\u308c\u305f\u30e9\u30d7\u30e9\u30b9\u6f14\u7b97\u5b50\u3067\u3059\u3002\u3053\u306e\u6f14\u7b97\u5b50\u306f\u3001\uff08\u8907\u96d1\u306a\uff09\u30db\u30c3\u30b8\u7406\u8ad6\u3067\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002       (adsbygoogle = window.adsbygoogle || 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