ON THE SPECIAL FINSLER METRIC

Title & Authors
ON THE SPECIAL FINSLER METRIC
Lee, Nan-Y;

Abstract
Given a Riemannian manifold (M, $\small{\alpha}$) with an almost Hermitian structure f and a non-vanishing covariant vector field b, consider the generalized Randers metric $\small{L\;=\;{\alpha}+{\beta}}$, where $\small{\beta}$ is a special singular Riemannian metric defined by b and f. This metric L is called an (a, b, f)-metric. We compute the inverse and the determinant of the fundamental tensor ($\small{g_{ij}}$) of an (a, b, f)-metric. Then we determine the maximal domain D of $\small{TM{\backslash}O}$ for an (a, b, f)-manifold where a y-local Finsler structure L is defined. And then we show that any (a, b, f)-manifold is quasi-C-reducible and find a condition under which an (a, b, f)-manifold is C-reducible.
Keywords
Finsler metric;generalized Randers metric;(a, b, f)-metric;Rizza manifold;C-reducible;
Language
English
Cited by
1.
An almost paracontact structure on a Rizza manifold, Comptes Rendus Mathematique, 2011, 349, 11-12, 683
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