University of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05003120220701On new classes of stretch Finsler metrics8699166910.22098/jfga.2022.10115.1058ENLaszlo KozmaInstitute of Mathematics, University of Debrecen, H-4002 Debrecen, Pf. 400,
Hungary0000-0002-4940-4028Sameer AnnonAbbasDoctoral School of Mathematical and Computational Sciences, Institute of
Mathematics, University of Debrecen, H-4002 Debrecen, Pf. 400, HungaryJournal Article20220110In this paper, we introduce two classes of stretch Finsler metrics. A Finsler metric with vanishing stretch <strong>B</strong><sup>∼</sup>-curvature ( stretch <strong>H</strong>-curvature) is called <strong>B</strong><sup>∼</sup>-stretch (<strong>H</strong>-stretch) metric (respectively). The class of <strong>B</strong><sup>∼</sup>-stretch (<strong>H</strong>-stretch) metric contain the class of Berwald (weakly Berwald) metric (respectively). First, we show that every complete <strong>B</strong><sup>∼</sup>-stretch metric (<strong>H</strong>-stretch metric) is a <strong>B</strong><sup>∼</sup>-metric (<strong>H</strong>-metric). Then we prove that every compact Finsler manifold with non-negative (non-positive) relatively isotropic stretch <strong>B</strong><sup>∼</sup>-curvature (stretch <strong>H</strong>-curvature) is <strong>B</strong><sup>∼</sup>-metric (<strong>H</strong>-metric).https://jfga.uma.ac.ir/article_1669_b761450e56bc457c2aa2c6cca778a120.pdf