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

Authors : Mosayeb ZOHREHVAND

Pages : 153-159

Doi:10.36890/iejg.1037651

View : 12 | Download : 4

Publication Date : 2022-04-30

Article Type : Research Paper

Abstract :Let $insert ignore into journalissuearticles values(M_n,g);$ 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 insert ignore into journalissuearticles values(IFHP); transformations on $TM_n$ with respect to the Levi-Civita connection of the deformed complete lift metric $\tilde{G}_f=g^C+insert ignore into journalissuearticles values(fg);^V$, 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 $insert ignore into journalissuearticles values(TM_n,\tilde{G}_f);$ is reduced to an affine and induces an infinitesimal affine transformation on $insert ignore into journalissuearticles values(M_n,g);$.
Keywords : Complete lift metric, Infinitesimal fiber preserving transformation, Infinitesimal holomorphically projective transformations, adapted almost complex structure