Some Locally Projectively Flat With (𝜶, 𝜷) Metric

Abstract

This paper has been devoted to the study of Some locally projectively flat with (𝛼, 𝛽) matric. In this paper first section is introductory. In the second section we have studied locally projectively flat with- (𝛼, 𝛽) metric. In this section we have studied some related definitions on projective change and locally projectively flat and using the relation: 2F(V.K. Kropina [9]), (called Kropina metric),  2F (M. Matsumoto [10]), and      2 F (M. Matsumoto [11]) where 𝛼 is a Riemannian matric and 𝛽 is a 1-form defined on the n-dimensional differentiable manifold M. In the light of these observations we get some results when 𝐹 and 𝛼 be locally projectively flat.

Keywords: Locally projectively flat, Projective change