On special types of minimal and totally geodesic unit vector fields
Differential Geometry
2007-05-23 v1
Abstract
We present a new equation with respect to a unit vector field on Riemannian manifold such that its solution defines a totally geodesic submanifold in the unit tangent bundle with Sasaki metric and apply it to some classes of unit vector fields. We introduce a class of covariantly normal unit vector fields and prove that within this class the Hopf vector field is a unique global one with totally geodesic property. For the wider class of geodesic unit vector fields on a sphere we give a new necessary and sufficient condition to generate a totally geodesic submanifold in .
Cite
@article{arxiv.math/0510002,
title = {On special types of minimal and totally geodesic unit vector fields},
author = {Alexander Yampolsky},
journal= {arXiv preprint arXiv:math/0510002},
year = {2007}
}
Comments
15 Pages