Affine connections on singular warped products
Differential Geometry
2021-06-02 v1
Abstract
In this paper, we introduce semi-symmetric metric Koszul forms and semi-symmetric non-metric Koszul forms on singular semi-Riemannian manifolds. Semi-symmetric metric Koszul forms and semi-symmetric non-metric Koszul forms and their curvature of semi-regular warped products are expressed in terms of those of the factor manifolds. We also introduce Koszul forms associated to the almost product structure on singular almost product semi-Riemannian manifolds. Koszul forms associated to the almost product structure and their curvature of semi-regular almost product warped products are expressed in terms of those of the factor manifolds. Furthermore, we generalize the results in \cite{St2} to singular multiply warped products.
Cite
@article{arxiv.2011.11209,
title = {Affine connections on singular warped products},
author = {Yong Wang},
journal= {arXiv preprint arXiv:2011.11209},
year = {2021}
}