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ВИДЕОТЕКА |
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Locally conformally Kaehler structures on homogeneous spaces Keizo Hasegawa Niigata University |
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Аннотация: A homogeneous Hermitian manifold We show as a main result a structure theorem of compact homogeneous l.c.K. manifolds, asserting that it has a structure of a holomorphic principal fiber bundle over a flag manifold with fiber a 1-dimensional complex torus. As an application of the theorem, we see that only compact homogeneous l.c.K. manifolds of complex dimension 2 are Hopf surfaces of homogeneous type. We also see that there exist no compact complex homogeneous l.c.K. manifolds; in particular neither complex Lie groups nor complex paralellizable manifolds admit their compatible l.c.K. structures. We show as a main result a structure theorem of compact homogeneous l.c.K. manifolds, asserting that it has a structure of a holomorphic principal fiber bundle over a flag manifold with fiber a 1-dimensional complex torus. As an application of the theorem, we see that only compact homogeneous l.c.K. manifolds of complex dimension 2 are Hopf surfaces of homogeneous type. We also see that there exist no compact complex homogeneous l.c.K. manifolds; in particular neither complex Lie groups nor complex paralellizable manifolds admit their compatible l.c.K. structures. This talk is based on a joint work with Y. Kamishima “Locally conformally Kaehler structures on homogeneous spaces” (arXiv:1101.3693). Язык доклада: английский |