Geodesic
Conformal Killing graphs in foliated Riemannian spaces with density: rigidity and stability
Commentationes Mathematicae Universitatis Carolinae, Tome 62 (2021) no. 2, pp. 175-200.

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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.
DOI : 10.14712/1213-7243.2021.017
Classification : 53C42
Keywords: weighted Riemannian manifold; conformal Killing graph; $f$-mean curvature; Bakry--Émery--Ricci tensor; strong $f$-stability 
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     title = {Conformal {Killing} graphs in foliated {Riemannian} spaces with density: rigidity and stability},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {175--200},
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Velásquez, Marco L. A.; Ramalho, André F. A.; de Lima, Henrique F.; Santos, Márcio S.; Oliveira, Arlandson M. S. Conformal Killing graphs in foliated Riemannian spaces with density: rigidity and stability. Commentationes Mathematicae Universitatis Carolinae, Tome 62 (2021) no. 2, pp. 175-200. doi : 10.14712/1213-7243.2021.017. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2021.017/

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