Notes on totally geodesic foliations of a complete semi-Riemannian manifold

Authors

AN SOOK SHIN
HYELIM HAN
HOBUM KIM

DOI

10.55730/1300-0098.3376

Abstract

In this paper, we prove that the orthogonal complement $\mathcal{F}^{\perp}$ of a totally geodesic foliation $\mathcal{F}$ on a complete semi-Riemannian manifold $(M,g)$ satisfying a certain inequality between mixed sectional curvatures and the integrability tensor of $\mathcal{F}^{\perp}$ is totally geodesic. We also obtain conditions for the existence of totally geodesic foliations on a complete semi-Riemannian manifold $(M,g)$ with bundle-like metric $g$.

Keywords

Complete semi-Riemannian manifold, totally geodesic foliation, mixed sectional curvature

First Page

528

Last Page

536

Recommended Citation

SHIN, AN SOOK; HAN, HYELIM; and KIM, HOBUM (2023) "Notes on totally geodesic foliations of a complete semi-Riemannian manifold," Turkish Journal of Mathematics: Vol. 47: No. 2, Article 8. https://doi.org/10.55730/1300-0098.3376
Available at: https://journals.tubitak.gov.tr/math/vol47/iss2/8