Conformal fields and the stability of leaves with constant higher order mean curvature

Details Conformal fields and the stability of leaves with constant higher order mean curvature Conformal fields and the stability of leaves with constant higher order mean curvature

2009-11-17

arxiv.org/abs/0911.3294v1

Mathematics

Differential Geometry

Scientific paper

In this paper, we study submanifolds with constant $r$th mean curvature $S_r$. We investigate, the stability of such submanifolds in the case when they are leaves of a codimension one foliation. We also generalize recent results by Barros - Sousa and Al\'{i}as - Colares, concerning conformal fields, to an arbitrary manifold. Using this we show that normal component of a Killing field is a $r$th Jacobi field of a submanifold with $S_{r+1}$ constant. Finally, we study relations between $r$th Jacobi fields and vector fields preserving a foliation.

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