Titlebook: An Introduction to Riemann-Finsler Geometry; D. Bao,S.-S. Chern,Z. Shen Textbook 2000 Springer Science+Business Media New York 2000 Calc.D

Colonnade

https://doi.org/10.1007/978-3-658-14309-1In §3.9, we encountered the flag curvature. As the name suggests, this quantity (denoted .) involves a location . ϵ ., a flagpole ℓ:= with . ϵ ..., and a transverse edge . ϵ .... The precise formula is quite elegantly given by (3.9.3): ..

maverick

https://doi.org/10.1007/978-3-8349-8493-7A .. 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 ..

袋鼠

Anticonvulsants

grudging

Curvature and Schur’s LemmaThe curvature 2-forms of the Chern connection are ..

皱痕

真实的人

The Cartan—Hadamard Theorem and Rauch’s First TheoremIn §5.5, we estimated the growth of certain Jacobi fields using the first few terms of a power series. That was valid only for a short time interval. In the present section, we use a more delicate approach—known as a comparison argument. The resulting estimate holds for long time intervals.

刚开始

青春期

Nonconformist

Constant Flag Curvature Spaces and Akbar-Zadeh’s TheoremIn §3.9, we encountered the flag curvature. As the name suggests, this quantity (denoted .) involves a location . ϵ ., a flagpole ℓ:= with . ϵ ..., and a transverse edge . ϵ .... The precise formula is quite elegantly given by (3.9.3): ..