IFHP Transformations on the Tangent Bundle of a Riemannian Manifold with a Class of Pseudo-Riemannian Metrics

Zohrehvand, Mosayeb

doi:10.7546/crabs.2020.02.04

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2022

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“…The notion of infinitesimal holomorphically projective transformations is introduced by S. Ishihara in [10] and after that many authors studied them on manifolds, e.g. [5,7,8,9,12,13,18]. Now let φ be a transformation on T M n .…”

Section: Introductionmentioning

confidence: 99%

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

Zohrehvand

2022

International Electronic Journal of Geometry

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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 $(M_n,g)$.

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