Titlebook: Comparison Finsler Geometry; Shin-ichi Ohta Book 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer

Myocarditis

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

dendrites

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

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

爱国者

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.

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