In this paper, we first show that the complete lift $U^{c}$ to $TM$ of a vector field $U$ on $M$ is an infinitesimal fiber-preserving conformal transformation if and only if $U$ is an infinitesimal homothetic transformation of $(M,g)$. Here, $(M, g)$ is a Riemannian manifold and $TM$ is its tangent bundle with a Mus-Cheeger-Gromoll type metric $\tilde{g}$. Secondly, we search for some conditions under which $\left(\overset{h}{\nabla},\tilde{g}\right)$ is a Codazzi pair on $TM$ when $(\nabla, g)$ is a Codazzi pair on $M$ where $\overset{h}{\nabla}$ is the horizontal lift of a linear connection $\nabla$ on $M$. We finally discuss the need for further research.
Codazzi pair infinitesimal fiber-preserving conformal transformation infinitesimal homothetic transformation Mus-Cheeger-Gromoll type metric tangent bundle
Primary Language | English |
---|---|
Subjects | Mathematical Sciences |
Journal Section | Research Article |
Authors | |
Publication Date | March 31, 2023 |
Submission Date | August 25, 2022 |
Published in Issue | Year 2023 Issue: 42 |
|