Statistical structures and Killing vector fields on tangent bundles with respect to two different metrics

IF 0.7 Q2 MATHEMATICS
Murat ALTUNBAŞ
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引用次数: 0

Abstract

Let $(M,g)$ be a Riemannian manifold and $TM$ be its tangent bundle. The purpose of this paper is to study statistical structures on $TM$ with respect to the metrics $G_{1}=^{c}g+^{v}(fg)$ and $G_{2}=^{s}g_{f}+^{h}g,\ $ where $f$ is a smooth function on $M,$ $^{c}g$ is the complete lift of $g$, $^{v}(fg)$ is the vertical lift of $fg$, $^{s}g_{f}$ is a metric obtained by rescaling the Sasaki metric by a smooth function $f$ and $^{h}g$ is the horizontal lift of $g.$ Moreover, we give some results about Killing vector fields on $TM$ with respect to these metrics.
关于两个不同度量的切束上的统计结构和消去向量场
设$(M,g)$是一个黎曼流形,$TM$是它的切线束。本文的目的是研究$TM$上关于度量$G_{1}=^{c}g+^{v}(fg)$和$G_{2}=^{s} G_{f}+^{h}g的统计结构,其中$f$是$M上的光滑函数,$ $^{c}g$是$g$的完全升力,$ ^{v}(fg)$是$fg$的垂直升力,$ ^{s} G_{f}$是用光滑函数$f$重新标称Sasaki度量得到的一个度量,$ ^{h}g$是$g的水平升力。此外,我们给出了关于这些度量在TM上消灭向量场的一些结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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