Turkish Journal of Mathematics
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 $g$.
DOI
10.55730/1300-0098.3376
Keywords
Complete semi-Riemannian manifold, totally geodesic foliation, mixed sectional curvature
First Page
528
Last Page
536
Recommended Citation
SHIN, A. S, HAN, H, & KIM, H (2023). Notes on totally geodesic foliations of a complete semi-Riemannian manifold. Turkish Journal of Mathematics 47 (2): 528-536. https://doi.org/10.55730/1300-0098.3376
