Immersions of Riemannian manifolds with a given normal bundle structure. I
Oldřich Kowalski (1969)
Czechoslovak Mathematical Journal
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Oldřich Kowalski (1969)
Czechoslovak Mathematical Journal
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Gérard Besson, Manlio Bordoni (1990)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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In this Note we give a rule to compute explicitely the spectrum and the eigenfunctions of the total space of a Riemannian submersion with totally geodesic fibers, in terms of the spectra and eigenfunctions of the typical fiber and any associated principal bundle.
Mohamed Tahar Kadaoui Abbassi, Maâti Sarih (2005)
Archivum Mathematicum
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There is a class of metrics on the tangent bundle of a Riemannian manifold (oriented , or non-oriented, respectively), which are ’naturally constructed’ from the base metric [Kow-Sek1]. We call them “-natural metrics" on . To our knowledge, the geometric properties of these general metrics have not been studied yet. In this paper, generalizing a process of Musso-Tricerri (cf. [Mus-Tri]) of finding Riemannian metrics on from some quadratic forms on to find metrics (not necessary...
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...
Kamil Niedziałomski (2012)
Archivum Mathematicum
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Let be a Riemannian manifold, its frame bundle. We construct new examples of Riemannian metrics, which are obtained from Riemannian metrics on the tangent bundle . We compute the Levi–Civita connection and curvatures of these metrics.