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Journals / Hacettepe Journal of Mathematics and Statistics / 2006 / Cilt: 35 - Sayı: 2

INFINITESIMAL AFFINE TRANSFORMATIONS IN THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD WITH RESPECT TO THE HORIZONTAL LIFT OF AN AFFINE CONNECTION

A. GEZER
K. AKBULUT
Pages
155–159
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

The main purpose of the present paper is to study properties of vertical infinitesimal affine transformation in the tangent bundle of a Riemannian manifold with respect to the horizontal lift of an affine connection, and to apply the results obtained to the study of fibre-preserving infinitesimal affine transformations in this setting.

📌 3 Key Takeaways

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Objective & Hypothesis:The main purpose of the present paper is to study properties of vertical infinitesimal affine transformation in the tangent bundle of a Riemannian manifold with respect to the horizontal lift of an affine connection, and to apply the results obtained to the study of fibre-preserving infinitesimal affine transformations in this setting.
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Key Findings & Data:The main purpose of the present paper is to study properties of vertical infinitesimal affine transformation in the tangent bundle of a Riemannian manifold with respect to the horizontal lift of an affine connection, and to apply the results obtained to the study of fibre-preserving infinitesimal affine transformations in this setting.
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Conclusion & Impact:The main purpose of the present paper is to study properties of vertical infinitesimal affine transformation in the tangent bundle of a Riemannian manifold with respect to the horizontal lift of an affine connection, and to apply the results obtained to the study of fibre-preserving infinitesimal affine transformations in this setting.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Lift · Tangent bundle · Infinitesimal affine transformation

Abstract

The main purpose of the present paper is to study properties of vertical infinitesimal affine transformation in the tangent bundle of a Riemannian manifold with respect to the horizontal lift of an affine connection, and to apply the results obtained to the study of fibre-preserving infinitesimal affine transformations in this setting.

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Cite This Article

GEZER, A., AKBULUT, K. (2022). INFINITESIMAL AFFINE TRANSFORMATIONS IN THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD WITH RESPECT TO THE HORIZONTAL LIFT OF AN AFFINE CONNECTION. Hacettepe Journal of Mathematics and Statistics, Cilt: 35 - Sayı: 2, 155–159. https://ajindex.com/articles/530762

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References (2)

  1. Yano K. and Ishihara, S. Tangent and cotangent bundles (Marcel Dekker, New York, 1973).
  2. Magden A. and Salimov, A. A. Horizontal lifts of tensor fields to sections of the tangent bundle. (in Russian) Izv. Vyssh. Uchebn. Zaved. Mat. 3, 77–80, 2001. Kobayashi S. and Nomizu K. Foundations of Differential Geometry (Wiley-Inter Science Publications, New York, 1963).