竞选运动
发表于 2025-3-26 22:04:00
Riemannian Manifolds and Two of Hopf’s TheoremsA .. on a manifold . is a family of inner products {..}.∈. such that the quantities . are smooth in local coordinates. The Finsler function .(.) of a Riemannian manifold has the characteristic structure ..
煞费苦心
发表于 2025-3-27 03:57:54
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表两个
发表于 2025-3-27 06:12:48
Graduate Texts in Mathematicshttp://image.papertrans.cn/a/image/155463.jpg
sed-rate
发表于 2025-3-27 09:44:40
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libertine
发表于 2025-3-27 17:14:32
Finsler Surfaces and a Generalized Gauss-Bonnet Theorems, we only use objects which are invariant under positive rescaling in .. Consequently, our treatment using natural coordinates on . can be regarded as occurring on the (projective) sphere bundle ., in the context of homogeneous coordinates.
Fermentation
发表于 2025-3-27 21:48:18
Variations of Arc Length, Jacobi Fields, the Effect of Curvatureiant differentiation. That is explored in a series of guided exercises at the end of 5.2. (Those exercises involve the second variation as well.) A systematic self-contained account can also be found in .
汇总
发表于 2025-3-28 00:44:54
The Gauss Lemma and the Hopf-Rinow Theoremtive there is the identity; see §5.3. Thus, for . small enough, not only does exp. makes sense, it is also diffeomorphic to S... The image set . is called a . in . centered at .. We later show why it can be said to have radius equal to ..
失误
发表于 2025-3-28 04:36:37
The Index Form and the Bonnet—Myers Theoremonstant speed geodesic . = exp.., 0 ⩽ . ⩽ . that emanates from . = σ(0) and terminates at . = σ(.). If there is no confusion, label its velocity field by . also. Let .. denote covariant differentiation along σ, with reference vector .. This concept was introduced in the Exercise portion of 5.2.
SUE
发表于 2025-3-28 07:41:58
The Chern Connections not a connection on the bundle . over .. Nevertheless, it serves Finsler geometry in a manner that parallels what the Levi-Civita (Christoffel) connection does for Riemannian geometry. This connection is on equal footing with, but is different from, those due to Cartan, Berwald, and Hashiguchi (to
拾落穗
发表于 2025-3-28 12:08:03
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