Address:
Corresponding author: H.R. Salimi Moghaddam, Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, 81746-73441 Iran
Physics Group, Faculty of Basic Sciences Imam Ali University, Tehran, Iran
E-mail:
hr.salimi@sci.ui.ac.ir
salimi.moghaddam@gmail.com
m_parhizkar66@yahoo.com
m.parhizkar@uma.ac.ir
Abstract: In the present paper we study naturally reductive homogeneous $(\alpha ,\beta )$-metric spaces. We show that for homogeneous $(\alpha ,\beta )$-metric spaces, under a mild condition, the two definitions of naturally reductive homogeneous Finsler space, given in the literature, are equivalent. Then, we compute the flag curvature of naturally reductive homogeneous $(\alpha ,\beta )$-metric spaces.
AMSclassification: primary 53C60; secondary 53C30.
Keywords: naturally reductive homogeneous space, invariant Riemannian metric, invariant (\alpha ,\beta )-metric.
DOI: 10.5817/AM2021-1-1