Anthropoid
发表于 2025-3-23 10:43:40
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Obloquy
发表于 2025-3-23 16:37:30
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.
Allure
发表于 2025-3-23 20:57:54
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.
Saline
发表于 2025-3-23 23:28:55
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FLAG
发表于 2025-3-24 05:15:19
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Anticonvulsants
发表于 2025-3-24 09:16:55
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.
uncertain
发表于 2025-3-24 13:14:28
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Congestion
发表于 2025-3-24 17:55:27
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.
innate
发表于 2025-3-24 21:19:28
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Aspiration
发表于 2025-3-25 00:57:49
6楼