Embedded hypersurfaces with constant $m^{\text{th}}$ mean curvature in a unit sphere

Details Embedded hypersurfaces with constant $m^{\text{th}}$ mean curvature in a unit sphere Embedded hypersurfaces with constant $m^{\text{th}}$ mean curvature in a unit sphere

2009-04-02

arxiv.org/abs/0904.0299v1

Mathematics

Differential Geometry

Scientific paper

In this paper, we study $n$-dimensional hypersurfaces with constant $m^{\text{th}}$ mean curvature in a unit sphere $S^{n+1}(1)$ and construct many compact nontrivial embedded hypersurfaces with constant $m^{\text{th}}$ mean curvature $H_m>0$ in $S^{n+1}(1)$, for $1\leq m\leq n-1$. In particular, if the $4^{\text{th}}$ mean curvature $H_4$ takes value between $\dfrac{1}{(\tan \frac{\pi}{k})^4}$ and $\dfrac{k^4-4}{n(n-4)}$ for any integer $k\geq3$, then there exists an $n$-dimensional ($n\geq 5$) compact nontrivial embedded hypersurface with constant $H_4$ in $S^{n+1}(1)$.

Affiliated with

Also associated with

No associations

Rating

Embedded hypersurfaces with constant $m^{\text{th}}$ mean curvature in a unit sphere 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 Embedded hypersurfaces with constant $m^{\text{th}}$ mean curvature in a unit sphere, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Embedded hypersurfaces with constant $m^{\text{th}}$ mean curvature in a unit sphere will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-63423