On a new class of Finsler metrics

By Changtao Yu, Hongmei Zhu. 2011

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Abstract In this paper, the geometric meaning of ( α , β ) -norms is made clear. On this basis, a new class of Finsler metrics called general ( α , β ) -metrics are introduced, which are defined by a Riemannian metric and a 1-form. These metrics not only generalize ( α , β ) -metrics naturally, but also include some metrics structured by R. Bryant. The spray coefficients formula of some kinds of general ( α , β ) -metrics is given and the projective flatness is also discussed.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/575f57e27f1e36d6876ba5237aeac91dbe0073e4