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Titlebook: CR Submanifolds of Kaehlerian and Sasakian Manifolds; Kentaro Yano,Masahiro Kon Book 1983 Springer Science+Business Media New York 1983 ma

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https://doi.org/10.1007/978-3-319-59002-8ghborhood and x. local coordinates in U. If, from any system of coordinate neighborhoods covering the manifold M, we can choose a finite number of coordinate neighborhoods which cover the whole manifold, then M is said to be compact.
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Structures on Riemannian Manifolds,ghborhood and x. local coordinates in U. If, from any system of coordinate neighborhoods covering the manifold M, we can choose a finite number of coordinate neighborhoods which cover the whole manifold, then M is said to be compact.
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Submanifolds,he ambient manifold .to simplify the notation because it may cause no confusion. Let T(M) and T(M). denote the tangent and normal bundle of M respectively. The metric g and the connection .on .lead to invariant inner products and the connections on T(M) and T(M). We will define a connection on M explicitely.
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Submanifolds, of covariant differentiation in .and by g the Riemannian metric tensor field in .. Since the discussion is local, we may assume, if we want, that M is imbedded in .. The submanifold M is also a Riemannian manifold with Riemannian metric h given by h(X,Y) = g(X,Y) for any vector fields X and Y on M.
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