On new classes of stretch Finsler metrics

Document Type : Original Article

Authors

1 Institute of Mathematics, University of Debrecen, H-4002 Debrecen, Pf. 400, Hungary

2 Doctoral School of Mathematical and Computational Sciences, Institute of Mathematics, University of Debrecen, H-4002 Debrecen, Pf. 400, Hungary

Abstract

In this paper, we introduce two classes of stretch Finsler metrics. A Finsler metric with vanishing stretch  B∼-curvature ( stretch H-curvature) is called B∼-stretch (H-stretch) metric (respectively). The class of B∼-stretch (H-stretch) metric contain the class of Berwald (weakly Berwald) metric (respectively). First, we show that every complete B∼-stretch metric (H-stretch metric) is a B∼-metric (H-metric). Then we prove that every compact Finsler manifold with non-negative (non-positive) relatively isotropic stretch B∼-curvature (stretch H-curvature) is B∼-metric (H-metric).

Keywords

Journal of Finsler Geometry and its Applications
Volume 3, Issue 1
July 2022
Pages 86-99

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