Year 2020, Volume 13 , Issue 1, Pages 50 - 60 2020-01-30

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
Subjects Mathematics
Journal Section Research Article
Authors

Orcid: 0000-0002-3876-4060
Author: Mosayeb ZOHREHVAND
Country: Iran


Dates

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 <https://dergipark.org.tr/en/pub/iejg/issue/51297/566914>
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.