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arXiv · 1707.02768

On Concircular Transformations In Finsler Geometry

Zhongmin Shen·Guojun Yang
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Abstract

A geodesic circle in Finsler geometry is a natural extension of that in a Euclidean space. In this paper, we apply Lie derivatives and the Cartan $Y$-connection to study geodesic circles and (infinitesimal) concircular transformations on a Finsler manifold. We characterize a concircular vector field with some PDEs on the tangent bundle, and then we obtain respective necessary and sufficient conditions for a concircular vector field to be conformal and a conformal vector field to be concircular. We also show conditions for two conformally related Finsler metrics to be concircular, and obtain some invariant curvature properties under conformal and concircular transformations.

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Zhongmin Shen, Guojun Yang. 2017-07-10. On Concircular Transformations In Finsler Geometry. https://arxiv.org/abs/1707.02768

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