On extrinsic geometry of unit normal vector fields of Riemannian hyperfoliations

Details On extrinsic geometry of unit normal vector fields of Riemannian hyperfoliations On extrinsic geometry of unit normal vector fields of Riemannian hyperfoliations

2005-03-24

arxiv.org/abs/math/0503566v2

Publ. Math. Debrecen 63/4 (2003), 565 -- 567

Mathematics

Differential Geometry

13 pages

Scientific paper

We consider a unit normal vector field of (local) hyperfoliation on a given Riemannian manifold as a submanifold in the unit tangent bundle with Sasaki metric. We give an explicit expression of the second fundamental form for this submanifold and a rather simple condition its totally geodesic property in the case of a totally umbilic hyperfoliation. A corresponding example shows the non-triviality of this condition. In the 2-dimensional case, we give a complete description of Riemannian manifolds admitting a geodesic unit vector field with totally geodesic property.

Affiliated with

Also associated with

No associations

Rating

On extrinsic geometry of unit normal vector fields of Riemannian hyperfoliations 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 extrinsic geometry of unit normal vector fields of Riemannian hyperfoliations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On extrinsic geometry of unit normal vector fields of Riemannian hyperfoliations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-29477