On the problem of isometry of a hypersurface preserving mean curvature

Details On the problem of isometry of a hypersurface preserving mean curvature On the problem of isometry of a hypersurface preserving mean curvature

2007-03-20

arxiv.org/abs/math/0703580v1

Mathematics

Differential Geometry

11 pages

Scientific paper

The problem of determining the {\it Bonnet hypersurfaces in} $R^{n+1}$, for $n>1$, is studied here. These hypersurfaces are by definition those that can be isometrically mapped to another hypersurface or to itself (as locus) by at least one nontrivial isometry preserving the mean curvature. The other hypersurface and/or (the locus of) itself is called {\it Bonnet associate} of the initial hypersurface. The orthogonal net which is called \hbox{\it $A$-net} is special and very important for our study and it is described on a hypersurface. It is proved that, non-minimal hypersurface in $R^{n+1}$ with no umbilical points is a Bonnet hypersurface if and only if it has an $A$-net.

Affiliated with

Also associated with

No associations

Rating

On the problem of isometry of a hypersurface preserving mean curvature 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 the problem of isometry of a hypersurface preserving mean curvature, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the problem of isometry of a hypersurface preserving mean curvature will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-123464