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일반화 복소다양체 一般化された複素構造 Generalized complex structure
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In the field of mathematics known as differential geometry, a generalized complex structure is a property of a differential manifold that includes as special cases a complex structure and a symplectic structure. Generalized complex structures were introduced by Nigel Hitchin in 2002 and further developed by his students and . 미분기하학에서 일반화 복소다양체(一般化複素多樣體, 영어: generalized complex manifold)는 복소다양체와 심플렉틱 다양체의 공통적인 일반화이다. 물리학적으로, 캘브-라몽 장 가 존재하는 IIB 초끈 이론 축소화를 나타낸다. 数学の微分幾何学において、一般化された複素構造(いっぱんかされたふくそこうぞう、英: generalized complex structure)とは、可微分多様体の持つある種の性質をいう。その特別な場合として複素構造やシンプレクティック構造が現れることがある。一般化された複素構造は、2002年ににより導入され、さらに彼の学生であったとにより発展した。 最初は、この構造は微分形式の汎函数による特徴付けというヒッチンのプログラムから発生した。この構造は、2004年のロベルト・ダイクラーフ、、とカムラン・ヴァッファの位相弦の理論は位相的M-理論の特別な場合ではないかという提案の基礎となった。今日、一般化された複素構造は、物理的な弦理論で超対称性をもつで主要な役目を果たしている。フラックスコンパクト化は、10次元の物理を4-次元の我々のような世界へ関連付けるのであるが、(ツイストする必要がある)一般化された複素構造を必要とする。
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미분기하학에서 일반화 복소다양체(一般化複素多樣體, 영어: generalized complex manifold)는 복소다양체와 심플렉틱 다양체의 공통적인 일반화이다. 물리학적으로, 캘브-라몽 장 가 존재하는 IIB 초끈 이론 축소화를 나타낸다. 数学の微分幾何学において、一般化された複素構造(いっぱんかされたふくそこうぞう、英: generalized complex structure)とは、可微分多様体の持つある種の性質をいう。その特別な場合として複素構造やシンプレクティック構造が現れることがある。一般化された複素構造は、2002年ににより導入され、さらに彼の学生であったとにより発展した。 最初は、この構造は微分形式の汎函数による特徴付けというヒッチンのプログラムから発生した。この構造は、2004年のロベルト・ダイクラーフ、、とカムラン・ヴァッファの位相弦の理論は位相的M-理論の特別な場合ではないかという提案の基礎となった。今日、一般化された複素構造は、物理的な弦理論で超対称性をもつで主要な役目を果たしている。フラックスコンパクト化は、10次元の物理を4-次元の我々のような世界へ関連付けるのであるが、(ツイストする必要がある)一般化された複素構造を必要とする。 In the field of mathematics known as differential geometry, a generalized complex structure is a property of a differential manifold that includes as special cases a complex structure and a symplectic structure. Generalized complex structures were introduced by Nigel Hitchin in 2002 and further developed by his students and . These structures first arose in Hitchin's program of characterizing geometrical structures via functionals of differential forms, a connection which formed the basis of Robbert Dijkgraaf, Sergei Gukov, Andrew Neitzke and Cumrun Vafa's 2004 proposal that topological string theories are special cases of a topological M-theory. Today generalized complex structures also play a leading role in physical string theory, as supersymmetric flux compactifications, which relate 10-dimensional physics to 4-dimensional worlds like ours, require (possibly twisted) generalized complex structures.
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