Myocarditis
发表于 2025-3-30 08:21:54
https://doi.org/10.1007/BFb0116611 introduce Berwald spaces, Hilbert and Funk geometries, and Teichmüller spaces and discuss their characteristic properties..We will revisit some of these examples in Chap. . in the context of measured Finsler manifolds (i.e., Finsler manifolds equipped with measures).
训诫
发表于 2025-3-30 12:48:27
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dendrites
发表于 2025-3-30 16:58:14
Properties of Geodesicstion for the energy functional. To this end, some important quantities such as the fundamental and Cartan tensors are introduced. We will see that the metric definition of geodesics coincides with the variational definition as solutions to the geodesic equation. We also prove the Finsler analogue of
Fsh238
发表于 2025-3-30 21:59:30
CurvatureThis argument goes back to Ludwig Berwald’s important posthumous paper..The appearance of a geodesic variation reminds us of a characterization of covariant derivatives by using the Riemannian metric .. associated with a vector field . whose integral curves are geodesics. In fact, this viewpoint le
厌恶
发表于 2025-3-31 04:02:53
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爱国者
发表于 2025-3-31 06:06:25
Variation Formulas for Arclength along geodesics, including the study of cut and conjugate points. The first variation formula is closely related to the geodesic equation, which was introduced as the Euler–Lagrange equation for the energy functional. The second variation formula will be related to the flag curvature.
名字的误用
发表于 2025-3-31 12:52:44
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推崇
发表于 2025-3-31 14:18:29
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