Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)Khayyam Journal of Mathematics2423-47885220190701On General $( alpha, beta)$-Metrics with Some Curvature Properties30398420510.22034/kjm.2019.84205ENBankteshwar TiwariDST-CIMS, Institute of Science, Banaras Hindu University, Varanasi-221005,
India.Ranadip GangopadhyayDST-CIMS, Institute of Science, Banaras Hindu University, Varanasi-221005,
India.0000-0003-0989-3143Ghanashyam Kr.PrajapatiLoknayak Jai Prakash Institute of Technology, Chhapra-841302, India.Journal Article20180924In this paper, we study a class of Finsler metric called general $(alpha, beta)$ metrics and obtain an equation that characterizes these Finsler metrics of almost vanishing H-curvature. As a consequence of this result, we prove that a general $(alpha, beta)$-metric has almost vanishing $H$-curvature if and only if it has almost vanishing $Xi$-curvature.http://www.kjm-math.org/article_84205_7a50131e4fbba322eb53ea4697d49b67.pdf