On new classes of stretch Finsler metrics

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).

کلیدواژه ها:

stretch curvature ، complete stretch metric ، Berwald curvature ، H-curvature ، relatively isotropic stretch curvature