Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2014; 51(1): 115-128

Printed January 1, 2014

https://doi.org/10.4134/BKMS.2014.51.1.115

Copyright © The Korean Mathematical Society.

On the second approximate Matsumoto metric

Akbar Tayebi, Tayebeh Tabatabaeifar, and Esmaeil Peyghan

University of Qom, University of Qom, Arak University

Abstract

In this paper, we study the second approximate Matsumoto metric $F=\alpha+\beta+\beta^2/\alpha+\beta^3/\alpha^2$ on a manifold $M$. We prove that $F$ is of scalar flag curvature and isotropic S-curvature if and only if it is isotropic Berwald metric with almost isotropic flag curvature.

Keywords: isotropic Berwald curvature, S-curvature, almost isotropic flag curvature

MSC numbers: 53C60, 53C25