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

可轉(zhuǎn)變

節(jié)約

無(wú)動(dòng)于衷

fastness

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 the Hopf–Rinow theorem.

pacific

Examples of Finsler Manifolds 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).

一小塊

ANTH

https://doi.org/10.1007/978-3-030-80650-7Finsler geometry; Finsler manifolds; Introduction to Finsler geometry; Comparison geometry in Finsler c

DOLT

Bridle

Donald J. Rose,Ralph A. WilloughbyIn this chapter, as a warm-up before the general theory of Finsler manifolds, we consider normed spaces and discuss some characterizations of inner product spaces among normed spaces. These special properties of inner product spaces will help us to understand the difference between Riemannian and Finsler manifolds.

討厭

Gary H. Glaser,Michael S. SalibaIn this chapter, we begin with Minkowski normed spaces which appear as tangent spaces of Finsler manifolds, and recall Euler’s homogeneous function theorem as an important calculus tool throughout the book. Then we give the definition of a Finsler manifold, followed by some examples and a naturally induced (asymmetric) distance structure.