2006/03/20 by G. S. Asanov, Asanov, G. S.
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #math.DG #math.MG
paper · pdf · doi:10.48550/arxiv.math/0603472
arxiv created 2006/03/20 · arxiv updated 2009/12/01
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.