Hypersurfaces with a canonical principal direction

Details Hypersurfaces with a canonical principal direction Hypersurfaces with a canonical principal direction

2011-10-10

arxiv.org/abs/1110.2201v1

Mathematics

Differential Geometry

Principal Direction, Constant Mean Curvature,Transnormal Functions, Closed conformal vector fields, 17 pages

Scientific paper

Given a vector field $X$ in a Riemannian manifold, a hypersurface is said to have a canonical principal direction relative to $X$ if the projection of $X$ onto the tangent space of the hypersurface gives a principal direction. We give different ways for building these hypersurfaces, as well as a number of useful characterizations. In particular, we relate them with transnormal functions and eikonal equations. With the further condition of having constant mean curvature (CMC) we obtain a characterization of the canonical principal direction surfaces in Euclidean space as Delaunay surfaces. We also prove that CMC constant angle hypersurfaces in a product $\mathbb{R}\times N$ are either totally geodesic or cylinders.

Affiliated with

Also associated with

No associations

Rating

Hypersurfaces with a canonical principal direction 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 Hypersurfaces with a canonical principal direction, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hypersurfaces with a canonical principal direction will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-471043