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3-Sasakian Manifolds,As with the last chapter we will give more of a survey and only a few proofs. Another survey of both history and recent work on 3-Sasakian manifolds is Boyer and Galicki .开始没有 发表于 2025-3-22 13:56:41
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https://doi.org/10.1007/978-1-4757-3604-5Differential Geometry; Differential Topology; Manifolds; Riemannian geometry; curvature; manifold漂浮 发表于 2025-3-22 23:35:59
Symplectic Manifolds,onal differentiable (..) manifold ..n together with a global 2-form Ω which is closed and of maximal rank, i.e., .Ω = 0, Ω. ≠ 0. By a .: (.., Ω.) → (.., Ω.) we mean a diffeomorphism . : .. → .. such that .*Ω. =Ω..Cardioplegia 发表于 2025-3-23 04:42:21
Contact Manifolds, manifold is orientable. Also . has rank 2. on the Grassmann algebra ∧ ... at each point . ∈ . and thus we have a 1-dimensional subspace, {. ∈ ...|.(...) = 0}, on which . ≠ 0 and which is complementary to the subspace on which . = 0. Therefore choosing .. in this subspace normalized by .(..) = 1 we have a global vector field . satisfying ..抛媚眼 发表于 2025-3-23 08:50:43
Associated Metrics,rtant for our study; many of these were already mentioned in Chapter 1. For more detail the reader is referred to Gray and Hervella , Kobayashi-Nomizu and Kobayashi-Wu ; also, despite its classical nature, the book of Yano contains helpful information on many of these structures.