Displaying similar documents to “Invariance of g -natural metrics on linear frame bundles”

On the geometry of frame bundles

Kamil Niedziałomski (2012)

Archivum Mathematicum

Similarity:

Let ( M , g ) be a Riemannian manifold, L ( M ) its frame bundle. We construct new examples of Riemannian metrics, which are obtained from Riemannian metrics on the tangent bundle T M . We compute the Levi–Civita connection and curvatures of these metrics.

On natural metrics on tangent bundles of Riemannian manifolds

Mohamed Tahar Kadaoui Abbassi, Maâti Sarih (2005)

Archivum Mathematicum

Similarity:

There is a class of metrics on the tangent bundle T M of a Riemannian manifold ( M , g ) (oriented , or non-oriented, respectively), which are ’naturally constructed’ from the base metric g [Kow-Sek1]. We call them “ g -natural metrics" on T M . 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 T M from some quadratic forms on O M × ℝ m to find metrics (not necessary...

On the completeness of total spaces of horizontally conformal submersions

Mohamed Tahar Kadaoui Abbassi, Ibrahim Lakrini (2021)

Communications in Mathematics

Similarity:

In this paper, we address the completeness problem of certain classes of Riemannian metrics on vector bundles. We first establish a general result on the completeness of the total space of a vector bundle when the projection is a horizontally conformal submersion with a bound condition on the dilation function, and in particular when it is a Riemannian submersion. This allows us to give completeness results for spherically symmetric metrics on vector bundle manifolds and eventually for...