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

S. K. Narasimhamurthy, D. M. Vasantha

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.

Keywords


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

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DOI: http://dx.doi.org/10.26713%2Fjims.v4i3.94

eISSN 0975-5748; pISSN 0974-875X