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| Adapted Metrics and Webster Curvature in Finslerian 2-Dimensional Geometry |
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Citation： |
M. Crasmareanu.Adapted Metrics and Webster Curvature in Finslerian 2-Dimensional Geometry[J].Chinese Annals of Mathematics B,2016,37(3):419~426 |
| Page view： 1321
Net amount： 1040 |
Authors： |
M. Crasmareanu; |
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| Abstract： |
The Webster scalar curvature is computed for the sphere bundle
$T_1S$ of a Finsler surface $(S, F)$ subject to the Chern-Hamilton
notion of adapted metrics. As an application, it is derived that in
this setting $(T_1S, g_{\rm Sasaki})$ is a Sasakian manifold
homothetic with a generalized Berger sphere, and that a natural
Cartan structure is arising from the horizontal $1$-forms and the
author associates a non-Einstein pseudo-Hermitian structure. Also,
one studies when the Sasaki type metric of $T_1S$ is generally
adapted to the natural co-frame provided by the Finsler structure. |
Keywords： |
Webster curvature, Finsler geometry, Sasakian type metric on tangent bundle, Sphere bundle, Adapted metric, Cartan structure, Pseudo-Hermitian structure |
Classification： |
53C60, 58B20, 53D10, 53C56 |
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