Colonnade
发表于 2025-3-25 07:18:08
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
发表于 2025-3-25 09:17:04
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
发表于 2025-3-25 15:12:38
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Anticonvulsants
发表于 2025-3-25 17:09:27
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grudging
发表于 2025-3-25 21:48:21
Curvature and Schur’s LemmaThe curvature 2-forms of the Chern connection are ..
皱痕
发表于 2025-3-26 00:37:41
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真实的人
发表于 2025-3-26 05:31:06
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
发表于 2025-3-26 11:00:19
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青春期
发表于 2025-3-26 15:48:35
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Nonconformist
发表于 2025-3-26 19:14:16
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): ..