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## Infinitesimal Projective Transformations on the Tangent Bundle of a Riemannian Manifold with a Class of Lift Metrics

#### Mosayeb ZOHREHVAND [1]

Let ‎$‎ (M,g)$ be a Riemannian manifold and ‎$‎ TM$ be its tangent bundle. ‎In the present paper‎, ‎we study infinitesimal projective transformations on $TM$ with respect to the Levi-Civita connection of a class of (pseudo-)Riemannian metrics ‎$‎‎\tilde{g}‎$ which is a generalization of the three classical lifts of the metric ‎$‎g$. We characterized this type of transformations and then ‎we prove that if $(TM,‎\tilde{g}‎)$ admits a non-affine infinitesimal projective transformation‎, ‎then $M$ and $TM‎‎$ are locally flat.
Lift metrics, infinitesimal projective transformations, Riemannian manifold, tangent bundle, locally flat
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Primary Language en Mathematics Research Article Orcid: 0000-0002-3876-4060Author: Mosayeb ZOHREHVAND Country: Iran Publication Date : January 30, 2020
 Bibtex @research article { iejg566914, journal = {International Electronic Journal of Geometry}, issn = {}, eissn = {1307-5624}, address = {}, publisher = {Kazım İLARSLAN}, year = {2020}, volume = {13}, pages = {50 - 60}, doi = {10.36890/iejg.566914}, title = {Infinitesimal Projective Transformations on the Tangent Bundle of a Riemannian Manifold with a Class of Lift Metrics}, key = {cite}, author = {ZOHREHVAND, Mosayeb} } APA ZOHREHVAND, M . (2020). Infinitesimal Projective Transformations on the Tangent Bundle of a Riemannian Manifold with a Class of Lift Metrics. International Electronic Journal of Geometry , 13 (1) , 50-60 . DOI: 10.36890/iejg.566914 MLA ZOHREHVAND, M . "Infinitesimal Projective Transformations on the Tangent Bundle of a Riemannian Manifold with a Class of Lift Metrics". International Electronic Journal of Geometry 13 (2020 ): 50-60 Chicago ZOHREHVAND, M . "Infinitesimal Projective Transformations on the Tangent Bundle of a Riemannian Manifold with a Class of Lift Metrics". International Electronic Journal of Geometry 13 (2020 ): 50-60 RIS TY - JOUR T1 - Infinitesimal Projective Transformations on the Tangent Bundle of a Riemannian Manifold with a Class of Lift Metrics AU - Mosayeb ZOHREHVAND Y1 - 2020 PY - 2020 N1 - doi: 10.36890/iejg.566914 DO - 10.36890/iejg.566914 T2 - International Electronic Journal of Geometry JF - Journal JO - JOR SP - 50 EP - 60 VL - 13 IS - 1 SN - -1307-5624 M3 - doi: 10.36890/iejg.566914 UR - https://doi.org/10.36890/iejg.566914 Y2 - 2019 ER - EndNote %0 International Electronic Journal of Geometry Infinitesimal Projective Transformations on the Tangent Bundle of a Riemannian Manifold with a Class of Lift Metrics %A Mosayeb ZOHREHVAND %T Infinitesimal Projective Transformations on the Tangent Bundle of a Riemannian Manifold with a Class of Lift Metrics %D 2020 %J International Electronic Journal of Geometry %P -1307-5624 %V 13 %N 1 %R doi: 10.36890/iejg.566914 %U 10.36890/iejg.566914 ISNAD ZOHREHVAND, Mosayeb . "Infinitesimal Projective Transformations on the Tangent Bundle of a Riemannian Manifold with a Class of Lift Metrics". International Electronic Journal of Geometry 13 / 1 (January 2020): 50-60 . https://doi.org/10.36890/iejg.566914 AMA ZOHREHVAND M . Infinitesimal Projective Transformations on the Tangent Bundle of a Riemannian Manifold with a Class of Lift Metrics. Int. Electron. J. Geom.. 2020; 13(1): 50-60. Vancouver ZOHREHVAND M . Infinitesimal Projective Transformations on the Tangent Bundle of a Riemannian Manifold with a Class of Lift Metrics. International Electronic Journal of Geometry. 2020; 13(1): 60-50.

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