IFHP Transformations on the Tangent Bundle with the Deformed Complete Lift Metric

Year 2022, Volume: 15 Issue: 1, 153 - 159, 30.04.2022

Mosayeb Zohrehvand

https://doi.org/10.36890/iejg.1037651

Abstract

Let $(M_n,g)$ be a Riemannian manifold and $TM_n$ the total space of its tangent bundle. In this paper, we determine the infinitesimal fiber-preserving holomorphically projective (IFHP) transformations on $TM_n$ with respect to the Levi-Civita connection of the deformed complete lift metric $\tilde{G}_f=g^C+(fg)^V$, where $f$ is a nonzero differentiable function on $M_n$ and $g^C$ and $g^V$ are the complete lift and the vertical lift of $g$ on $TM_n$, respectively. Morevore, we prove that every IFHP transformation on $(TM_n,\tilde{G}_f)$ is reduced to an affine and induces an infinitesimal affine transformation on $(M_n,g)$.

Keywords

Complete lift metric, Infinitesimal fiber-preserving transformation, Infinitesimal holomorphically projective transformations, adapted almost complex structure

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