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

Marco L. A. Velásquez; André F. A. Ramalho; Henrique F. de Lima; Márcio S. Santos; Arlandson M. S. Oliveira

Commentationes Mathematicae Universitatis Carolinae (2021)

  • Issue: 2, page 175-200
  • ISSN: 0010-2628

Abstract

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In this paper we investigate the geometry of conformal Killing graphs in a Riemannian manifold M ¯ f n + 1 endowed with a weight function f and having a closed conformal Killing vector field V with conformal factor ψ V , that is, graphs constructed through the flow generated by V and which are defined over an integral leaf of the foliation V ⊥ 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 M ¯ f n + 1 according to the behavior of ψ V . Finally, related to conformal Killing graphs immersed in M ¯ f n + 1 with constant f -mean curvature, we study the strong stability.

How to cite

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Velásquez, Marco L. A., et al. "Conformal Killing graphs in foliated Riemannian spaces with density: rigidity and stability." Commentationes Mathematicae Universitatis Carolinae (2021): 175-200. <http://eudml.org/doc/297769>.

@article{Velásquez2021,
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.},
author = {Velásquez, Marco L. A., Ramalho, André F. A., de Lima, Henrique F., Santos, Márcio S., Oliveira, Arlandson M. S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {weighted Riemannian manifold; conformal Killing graph; $f$-mean curvature; Bakry–Émery–Ricci tensor; strong $f$-stability},
language = {eng},
number = {2},
pages = {175-200},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Conformal Killing graphs in foliated Riemannian spaces with density: rigidity and stability},
url = {http://eudml.org/doc/297769},
year = {2021},
}

TY - JOUR
AU - Velásquez, Marco L. A.
AU - Ramalho, André F. A.
AU - de Lima, Henrique F.
AU - Santos, Márcio S.
AU - Oliveira, Arlandson M. S.
TI - Conformal Killing graphs in foliated Riemannian spaces with density: rigidity and stability
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2021
PB - Charles University in Prague, Faculty of Mathematics and Physics
IS - 2
SP - 175
EP - 200
AB - 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.
LA - eng
KW - weighted Riemannian manifold; conformal Killing graph; $f$-mean curvature; Bakry–Émery–Ricci tensor; strong $f$-stability
UR - http://eudml.org/doc/297769
ER -

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