Mohamed Tahar Kadaoui Abbassi ; Ibrahim Lakrini - On the completeness of total spaces of horizontally conformal submersions

cm:9548 - Communications in Mathematics, December 23, 2021, Volume 29 (2021), Issue 3 - https://doi.org/10.2478/cm-2021-0031
On the completeness of total spaces of horizontally conformal submersions

Authors: Mohamed Tahar Kadaoui Abbassi ; Ibrahim Lakrini

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 the class of Cheeger-Gromoll and generalized Cheeger-Gromoll metrics on vector bundle manifolds. Moreover, we study the completeness of a subclass of g-natural metrics on tangent bundles and we extend the results to the case of unit tangent sphere bundles. Our proofs are mainly based on techniques of metric topology and on the Hopf-Rinow theorem.


Volume: Volume 29 (2021), Issue 3
Published on: December 23, 2021
Imported on: May 11, 2022
Keywords: General Mathematics,[MATH]Mathematics [math]


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