Conformal Killing graphs in foliated Riemannian spaces with density: rigidity and stability

Autor: André F. A. Ramalho, Márcio S. Santos, Marco L. A. Velásquez, Henrique F. de Lima, Arlandson M. S. Oliveira
Rok vydání: 2021
Předmět:
Zdroj: Commentationes Mathematicae Universitatis Carolinae. 62:175-200
ISSN: 1213-7243
0010-2628
Popis: In this paper we investigate the geometry of conformal Killing graphs in a Riemannian manifold $\overline{M}_f^{ n+1}$ endowed with a weight function $f$ and having a closed conformal Killing vector field $V$ with conformal factor $\psi_V$, that is, graphs constructed through the flow generated by $V$ and which are defined over an integral leaf of the foliation $V^{\perp}$ orthogonal to $V$. For such graphs, we establish some rigidity results under appropriate constraints on the $f$-mean curvature. Afterwards, we obtain some stability results for $f$-minimal conformal Killing graphs of $ \overline{M}_f^{ n+1}$ according to the behavior of $ \psi_V$. Finally, related to conformal Killing graphs immersed in $\overline{M}_f^{n+1}$ with constant $f$-mean curvature, we study the strong stability.
Databáze: OpenAIRE