A Metric on the Manifold of Immersions and Its Riemannian Curvature.
Gerd Kainz (1984)
Monatshefte für Mathematik
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Displaying similar documents to “Curvature of the Induced Riemannian Metric on the Tangent Bundle of a Riemannian Manifold.”
A Metric on the Manifold of Immersions and Its Riemannian Curvature.
A Ricci flat pseudo-Riemannian metric on the tangent bundle of a Riemannian manifold
Neculai Papaghiuc (2001)
Colloquium Mathematicae
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We consider a certain pseudo-Riemannian metric G on the tangent bundle TM of a Riemannian manifold (M,g) and obtain necessary and sufficient conditions for the pseudo-Riemannian manifold (TM,G) to be Ricci flat (see Theorem 2).
On two natural Riemannian metrics on a tube.
Labbi, M.-L. (2007)
Balkan Journal of Geometry and its Applications (BJGA)
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Rigidity in non-negative curvature
Luis Guijarro, Peter Petersen (1997)
Annales scientifiques de l'École Normale Supérieure
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-natural metrics of constant curvature on unit tangent sphere bundles
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.
On curvatures of linear frame bundles with naturally lifted metrics.
Kowalski, O., Sekizawa, M. (2005)
Rendiconti del Seminario Matematico
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Curvatures of the diagonal lift from an affine manifold to the linear frame bundle
Oldřich Kowalski, Masami Sekizawa (2012)
Open Mathematics
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We investigate the curvature of the so-called diagonal lift from an affine manifold to the linear frame bundle LM. This is an affine analogue (but not a direct generalization) of the Sasaki-Mok metric on LM investigated by L.A. Cordero and M. de León in 1986. The Sasaki-Mok metric is constructed over a Riemannian manifold as base manifold. We receive analogous and, surprisingly, even stronger results in our affine setting.
On a class of contact Riemannian manifolds.
Cho, Jong Taek (2000)
International Journal of Mathematics and Mathematical Sciences
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A Note on Generalized Recurrent Riemannian Manifold
Mileva Prvanović (1993)
Matematički Vesnik
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On the problem whether the image of a given differentiable map into Riemannian manifold is contained in a submanifold with parallel second fundamental form.
Helmut Reckziegel (1981)
Journal für die reine und angewandte Mathematik
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The natural transformations between T-th order prolongation of tangent and cotangent bundles over Riemannian manifolds
Mariusz Plaszczyk (2015)
Annales UMCS, Mathematica
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If (M,g) is a Riemannian manifold then there is the well-known base preserving vector bundle isomorphism TM → T* M given by v → g(v,−) between the tangent TM and the cotangent T* M bundles of M. In the present note first we generalize this isomorphism to the one JrTM → JrTM between the r-th order prolongation JrTM of tangent TM and the r-th order prolongation JrT M of cotangent TM bundles of M. Further we describe all base preserving vector bundle maps DM(g) : JrTM → JrT* M depending...