On projective Riemann quadratic (PR-quadratic) Finsler metrics

Document Type : Original Article

Author

Department of Mathematics, Faculty of Science, University of Qom, Qom. Iran

Abstract

This paper focuses on Projective Riemann quadratic (PR-quadratic) Finsler metrics, which are a variant of the Finsler metric in Finsler geometry. The paper introduces a special class of PR-quadratic Finsler metrics, called SPR-quadratic Finsler metrics, which is closed under projective changes with respect to a fixed volume form on M. This class contains the class of Douglas-Weyl metrics and is a subset of the class of Weyl metrics. The paper shows that any SPR-quadratic Finsler metric has a scalar flag curvature and a PR-quadratic Finsler metric has a scalar curvature if and only if it is of SPR-quadratic type. The results presented in this paper contribute to a deeper understanding of the behavior of PR-quadratic Finsler metrics and provide insights into the geometric properties of these metrics.

Keywords

Journal of Finsler Geometry and its Applications

Articles in Press, Accepted Manuscript
Available Online from 16 April 2024

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