Transverse totally geodesic submanifolds of the tangent bundle
| dc.creator | Abbassi, Mohamed Tahar Kadaoui | |
| dc.creator | Yampolsky, Alexander | |
| dc.date | 2005-03-24 | |
| dc.date.accessioned | 2026-07-07T05:18:24Z | |
| dc.date.available | 2026-07-07T05:18:24Z | |
| dc.description | It is well-known that if $ξ$ is a smooth vector field on a given Riemannian manifold $M^n$ then $ξ$ naturally defines a submanifold $ξ(M^n)$ transverse to the fibers of the tangent bundle $TM^n$ with Sasaki metric. In this paper, we are interested in transverse totally geodesic submanifolds of the tangent bundle. We show that a transverse submanifold $N^l$ of $TM^n$ ($1 \leq l \leq n$) can be realized locally as the image of a submanifold $F^l$ of $M^n$ under some vector field $ξ$ defined along $F^l$. For such images $ξ(F^l)$, the conditions to be totally geodesic are presented. We show that these conditions are not so rigid as in the case of $l=n$, and we treat several special cases ($ξ$ of constant length, $ξ$ normal to $F^l$, $M^n$ of constant curvature, $M^n$ a Lie group and $ξ$ a left invariant vector field) | |
| dc.identifier | https://arxiv.org/abs/math/0503561 | |
| dc.identifier | http://arxiv.org/abs/math/0503561 | |
| dc.identifier | Publ. Math. Debrecen 64/1-2 (2004), 129-154 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74650 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53B25, 53C42 | |
| dc.title | Transverse totally geodesic submanifolds of the tangent bundle | |
| dc.type | text |