On Riemannian tangent bundles.
Al-Aqeel, Adnan, Bejancu, Aurel (2006)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Al-Aqeel, Adnan, Bejancu, Aurel (2006)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Oldřich Kowalski, Masami Sekizawa (2008)
Archivum Mathematicum
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In this paper we prove that each -natural metric on a linear frame bundle over a Riemannian manifold is invariant with respect to a lifted map of a (local) isometry of the base manifold. Then we define -natural metrics on the orthonormal frame bundle and we prove the same invariance result as above for . Hence we see that, over a space of constant sectional curvature, the bundle with an arbitrary -natural metric is locally homogeneous.
Druţă, S.L., Oproiu, V. (2010)
Balkan Journal of Geometry and its Applications (BJGA)
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Druţă, Simona-Luiza (2009)
Balkan Journal of Geometry and its Applications (BJGA)
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Eni, Cristian (2008)
Balkan Journal of Geometry and its Applications (BJGA)
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M. T. K. Abbassi, Giovanni Calvaruso (2012)
Archivum Mathematicum
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We completely classify Riemannian -natural metrics of constant sectional curvature on the unit tangent sphere bundle of a Riemannian manifold . Since the base manifold turns out to be necessarily two-dimensional, weaker curvature conditions are also investigated for a Riemannian -natural metric on the unit tangent sphere bundle of a Riemannian surface.