Marco L. A. Velásquez, André F. A. Ramalho, Henrique F. de Lima, Márcio S. Santos, Arlandson M. S. Oliveira
Conformal Killing graphs in foliated Riemannian spaces with density: rigidity and stability

Comment.Math.Univ.Carolin. 62,2 (2021) 175-200.

Abstract: 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.

Keywords: weighted Riemannian manifold; conformal Killing graph; f-mean curvature; Bakry-Émery-Ricci tensor; strong f-stability

DOI: DOI 10.14712/1213-7243.2021.017
AMS Subject Classification: 53C42