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Journals / International Electronic Journal of Geometry / 2026 / Volume: 15 Issue: 1

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

Mosayeb Zohrehvand(Malayer University)0000-0002-3876-4060
Pages
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Publication Date
2022-04-30
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

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 $(M_n,g)$.

📌 3 Key Takeaways

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Objective & Hypothesis:Let $(M_n,g)$ be a Riemannian manifold and $TM_n$ the total space of its tangent bundle.
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Key Findings & Data: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.
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Conclusion & Impact: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 $(M_n,g)$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Complete lift metric · Infinitesimal fiber-preserving transformation · Infinitesimal holomorphically projective transformations

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 $(M_n,g)$.

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Cite This Article

Zohrehvand, M. (2022). IFHP Transformations on the Tangent Bundle with the Deformed Complete Lift Metric. International Electronic Journal of Geometry, Volume: 15 Issue: 1. https://doi.org/10.36890/iejg.1037651

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