Browsing by Subject "flag curvature"

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    On Concircular Transformations in Finsler Geometry
    (Springer, 2019) Shen, Zhongmin; Yang, Guojun; Mathematical Sciences, School of Science
    A geodesic circle in Finsler geometry is a natural extension of that in a Euclidean space. In this paper, we 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 respectively 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.