Hypersurfaces of a Projective Randers conformal change

TL;DR

This paper investigates conditions under which a Randers conformal change in Finsler geometry preserves geodesic properties and projective flatness of hypersurfaces, extending classical results in Finsler space theory.

Contribution

It establishes new criteria for a Randers conformal change to be projective and for hypersurfaces to remain totally geodesic or become projectively flat under this change.

Findings

Conditions for a Randers conformal change to be projective.

Criteria for hypersurfaces to remain totally geodesic.

Conditions for hypersurfaces to be projectively flat.

Abstract

In the year 1984 Shibata investigated the theory of a change which is called a $ \beta $-change of a Finsler metric. On the other hand in 1985 a systematic study of geometry of hypersurfaces in Finsler spaces was given by Matsumoto. In the present paper is to devoted to the study of a condition for a Randers conformal change to be projective and find out when a totally geodesic hypersurface $ F^{n-1} $ remains to be a totally geodesic hypersurface $ F^{n-1} $ under the projective Randers conformal change. Further obatined the condition under which a Finslerian hypersurfaces given by the projective Randers conformal change are projectively flat.