On some sub-Riemannian objects in hypersurfaces of sub-Riemannian manifolds

Details On some sub-Riemannian objects in hypersurfaces of sub-Riemannian manifolds On some sub-Riemannian objects in hypersurfaces of sub-Riemannian manifolds

2007-01-15

arxiv.org/abs/math/0701401v2

Bull.Austral.Math.Soc.,Vol.70(2004),177-198

Mathematics

Differential Geometry

18 pages; some errors corrected

Scientific paper

We study some sub-Riemannian objects (such as horizontal connectivity, horizontal connection, horizontal tangent plane, horizontal mean curvature) in hypersurfaces of sub-Riemannian manifolds. We prove that if a connected hypersurface in a contact manifold of dimension more than three is noncharacteristic or with isolated characteristic points, then given two points, there exists at least one piecewise smooth horizontal curve in this hypersurface connecting them. In any sub-Riemannian manifold, we obtain the sub-Riemannian version of the fundamental theorem of Riemannian geometry. We use this nonholonomic connection to study horizontal mean curvature of hypersurfaces.

Affiliated with

Also associated with

No associations

Rating

On some sub-Riemannian objects in hypersurfaces of sub-Riemannian manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On some sub-Riemannian objects in hypersurfaces of sub-Riemannian manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On some sub-Riemannian objects in hypersurfaces of sub-Riemannian manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-585126