Finsleroid--Finsler Space with Berwald and Landsberg Conditions
Differential Geometry
2007-05-23 v1 Metric Geometry
Abstract
We formulate the notion of the Finsleroid--Finsler space, including the positive--definite as well as indefinite cases. The associated concepts of angle, scalar product, and the distance function are elucidated. If the Finsleroid--Finsler space is of Landsberg type, then the Finsleroid charge is a constant. The Finsleroid--Finsler space proves to be a Berwald space if and only if the Finsleroid--axis 1-form is parallel with respect to the associated Riemannian metric and, simultaneously, the Finsleroid charge is a constant. The necessary and sufficient conditions for the Finsleroid--Finsler space to be of the Landsberg type are found, which are explicit and simple. The structure of the associated curvature tensors has been elucidated.
Keywords
Cite
@article{arxiv.math/0603472,
title = {Finsleroid--Finsler Space with Berwald and Landsberg Conditions},
author = {G. S. Asanov},
journal= {arXiv preprint arXiv:math/0603472},
year = {2007}
}