2000 | OriginalPaper | Chapter
The Index Form and the Bonnet—Myers Theorem
Authors : D. Bao, S.-S. Chern, Z. Shen
Published in: An Introduction to Riemann-Finsler Geometry
Publisher: Springer New York
Included in: Professional Book Archive
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
Let (M, F) be a Finsler manifold, where F is C∞ on TM \0 and is positively (but perhaps not absolutely) homogeneous of degree 1. Fix T ∈ T p M. Consider the constant speed geodesic σ(t) = exp p (tT), 0 ⩽ t ⩽ r that emanates from p = σ(0) and terminates at q = σ(r). If there is no confusion, label its velocity field by T also. Let D T denote covariant differentiation along σ, with reference vector T. This concept was introduced in the Exercise portion of 5.2.