Projective Change between Randers Metric and Special $(\alpha, \beta)$-metric

Authors

  • S. K. Narasimhamurthy Department of Mathematics, Kuvempu University, Shankaraghatta 577451, Shivamogga, Karnataka, India
  • D. M. Vasantha Department of Mathematics, Kuvempu University, Shankaraghatta 577451, Shivamogga, Karnataka, India

DOI:

https://doi.org/10.26713/jims.v4i3.94

Keywords:

Projective change, Randers metric, Douglas metric, Projective invariant, Locally Minkowski space

Abstract

In the present paper, we find the conditions to characterize projective change between two $(\alpha, \beta)$-metrics, such as special $(\alpha, \beta)$-metric, $L=\alpha-\frac{\beta^2}{\alpha}+\beta$ and Randers metric $\bar{L}= \bar{\alpha}+\bar{\beta}$ on a manifold with dim $n \geq 3$, where $\alpha$ and $\bar{\alpha}$ are two Riemannian metrics, $\beta$ and $\bar{\beta}$ are two non-zero 1-forms. Further, we study the special curvature properties of two classes of $(\alpha, \beta)$-metrics.

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CITATION

How to Cite

Narasimhamurthy, S. K., & Vasantha, D. M. (2012). Projective Change between Randers Metric and Special $(\alpha, \beta)$-metric. Journal of Informatics and Mathematical Sciences, 4(3), 293–303. https://doi.org/10.26713/jims.v4i3.94

Issue

Vol. 4 No. 3 (2012)

Section

Research Articles

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