g-Natural metrics on unit tangent sphere bundles via a Musso-Tricerri process

g-Natural metrics on unit tangent sphere bundles via a Musso-Tricerri process

E. Musso and F. Tricerri had given a process of construction of Riemannian metrics on tangent bundles and unit tangent bundles, over m-dimensional Riemannian manifolds (M, g), from some special quadratic forms an OM × R^m and OM, respectively, where OM is the bundle of orthonormal frames [7]. We pr...

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Bibliographic Details
Main Author: Mohamed Tahar Kadaoui Abbassi
Format: Article
Language:English
Published: Sapienza Università Editrice 2010-01-01
Series:Rendiconti di Matematica e delle Sue Applicazioni
Subjects:
unit tangent (sphere) bundle
einstein manifold
g-natural metric
Online Access:https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2010(3-4)/239-247.pdf
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spelling doaj-0358f37f2b6345769ae3344ed33a3d5f2021-08-16T11:03:12ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33502010-01-01303-4239247g-Natural metrics on unit tangent sphere bundles via a Musso-Tricerri processMohamed Tahar Kadaoui Abbassi0Université Sidi Mohamed Ben AbdallahE. Musso and F. Tricerri had given a process of construction of Riemannian metrics on tangent bundles and unit tangent bundles, over m-dimensional Riemannian manifolds (M, g), from some special quadratic forms an OM × R^m and OM, respectively, where OM is the bundle of orthonormal frames [7]. We prove in this note that every Riemannian g-natural metric on the unit tangent sphere bundle over a Riemannian manifold can be constructed by the Musso-Tricerri’s process. As a corollary, we show that every Riemannian g-natural metric on the unit tangent bundle, over a two-point homogeneous space, is homogeneous.https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2010(3-4)/239-247.pdfunit tangent (sphere) bundleeinstein manifoldg-natural metric
collection DOAJ
language English
format Article
sources DOAJ
author Mohamed Tahar Kadaoui Abbassi
spellingShingle Mohamed Tahar Kadaoui Abbassi
g-Natural metrics on unit tangent sphere bundles via a Musso-Tricerri process
Rendiconti di Matematica e delle Sue Applicazioni
unit tangent (sphere) bundle
einstein manifold
g-natural metric
author_facet Mohamed Tahar Kadaoui Abbassi
author_sort Mohamed Tahar Kadaoui Abbassi
title g-Natural metrics on unit tangent sphere bundles via a Musso-Tricerri process
title_short g-Natural metrics on unit tangent sphere bundles via a Musso-Tricerri process
title_full g-Natural metrics on unit tangent sphere bundles via a Musso-Tricerri process
title_fullStr g-Natural metrics on unit tangent sphere bundles via a Musso-Tricerri process
title_full_unstemmed g-Natural metrics on unit tangent sphere bundles via a Musso-Tricerri process
title_sort g-natural metrics on unit tangent sphere bundles via a musso-tricerri process
publisher Sapienza Università Editrice
series Rendiconti di Matematica e delle Sue Applicazioni
issn 1120-7183
2532-3350
publishDate 2010-01-01
description E. Musso and F. Tricerri had given a process of construction of Riemannian metrics on tangent bundles and unit tangent bundles, over m-dimensional Riemannian manifolds (M, g), from some special quadratic forms an OM × R^m and OM, respectively, where OM is the bundle of orthonormal frames [7]. We prove in this note that every Riemannian g-natural metric on the unit tangent sphere bundle over a Riemannian manifold can be constructed by the Musso-Tricerri’s process. As a corollary, we show that every Riemannian g-natural metric on the unit tangent bundle, over a two-point homogeneous space, is homogeneous.
topic unit tangent (sphere) bundle
einstein manifold
g-natural metric
url https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2010(3-4)/239-247.pdf
work_keys_str_mv AT mohamedtaharkadaouiabbassi gnaturalmetricsonunittangentspherebundlesviaamussotricerriprocess
_version_ 1721205833035939840

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