Tangent bundle and indicatrix bundle of a Finsler manifold



Kodai Mathematical Journal
previous :: next

Tangent bundle and indicatrix bundle of a Finsler manifold

Aurel Bejancu

Source: Kodai Math. J. Volume 31, Number 2 (2008), 272-306.

Abstract

Let Fm = (M, F) be a Finsler manifold and G be the Sasaki-Finsler metric on TM°. We show that the curvature tensor field of the Levi-Civita connection on (TM°, G) is completely determined by the curvature tensor field of Vrănceanu connection and some adapted tensor fields on TM°. Then we prove that (TM°, G) is locally symmetric if and only if Fm is locally Euclidean. Also, we show that the flag curvature of the Finsler manifold Fm is determined by some sectional curvatures of the Riemannian manifold (TM°, G). Finally, for any c ≠ 0 we introduce the c-indicatrix bundle IM (c) and obtain new and simple characterizations of Fm of constant flag curvature c by means of geometric objects on both IM (c) and (TM°, G).

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.kmj/1214442799
Digital Object Identifier: doi:10.2996/kmj/1214442799
Mathematical Reviews number (MathSciNet): MR2435896

previous :: next

2008 © Tokyo Institute of Technology, Department of Mathematics