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Titlebook: Singular Semi-Riemannian Geometry; Demir N. Kupeli Book 1996 Springer Science+Business Media B.V. 1996 Riemannian geometry.Signatur.Tensor

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A Review of Covariant Derivative Operators in Complex Vector Bundlesy be found in [21]. For the same reason as in Section 2.5, that since there is a one-to-one correspondence between covariant derivative operators and connections, a covariant derivative operator will be called a connection. We will assume that every object in hand is smooth unless otherwise stated.
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Book 1996 fields are obtained purely from the algebraic point of view without referring to their geometric origin. Chapter II is devoted to a review of covariant derivative operators in real vector bundles. Chapter III is the main part of this book where, intrinsically, the Koszul connection is introduced an
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A Review of Covariant Derivative Operators in Complex Vector Bundlesy be found in [21]. For the same reason as in Section 2.5, that since there is a one-to-one correspondence between covariant derivative operators and connections, a covariant derivative operator will be called a connection. We will assume that every object in hand is smooth unless otherwise stated.
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Hermitian Submanifolds of Nondegenerate Kähler Manifoldsariant under . if and only if . is a complex submanifold of ., since the vanishing torsion tensor . of . on . implies that . is also vanishing on .. (see Theorem 6.2.2 for the details). Now, let . be a complex submanifold of a nondegenerate Kähler manifold (., ., .) of complex type (., .) and let ..
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Hermitian Submanifolds of Nondegenerate Kähler ManifoldsAlso note that, since . and N. are invariant under ., .┴ and .. are invariant under . and, therefore, we will use the same notation . for the restrictions of the canonical almost complex structure . of . to ., .┴ and ...
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