On submanifolds whose tubular hypersurfaces have constant mean curvatures

Details On submanifolds whose tubular hypersurfaces have constant mean curvatures On submanifolds whose tubular hypersurfaces have constant mean curvatures

2011-09-30

arxiv.org/abs/1109.6835v1

Mathematics

Differential Geometry

29 pages

Scientific paper

Motivated by the theory of isoparametric hypersurfaces, we study submanifolds whose tubular hypersurfaces have some constant "higher order mean curvatures". Here a $k$-th order mean curvature $Q_k$ ($k\geq1$) of a hypersurface $M^n$ is defined as the $k$-th power sum of the principal curvatures, or equivalently, of the shape operator. Many necessary restrictions involving principal curvatures, higher order mean curvatures and Jacobi operators on such submanifolds are obtained, which, among other things, generalize some classical results in the theory of isoparametric hypersurfaces given by E. Cartan, K. Nomizu, H. F. M{\"u}nzner, Q. M. Wang, \emph{etc.}. As an application, we finally get a geometrical filtration for the focal varieties of isoparametric functions on a complete Riemannian manifold.

Affiliated with

Also associated with

No associations

Rating

On submanifolds whose tubular hypersurfaces have constant mean curvatures 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 submanifolds whose tubular hypersurfaces have constant mean curvatures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On submanifolds whose tubular hypersurfaces have constant mean curvatures will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-669522