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:	Physics Combinatorics Killing vector field Weight function Flow (mathematics) General Mathematics Foliation (geology) Conformal map Mathematics::Differential Geometry Riemannian manifold Curvature Constant (mathematics)
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
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::5fabb3f0888d96beeb00b104ae9a288a https://doi.org/10.14712/1213-7243.2021.017 Zobrazit plný text záznamu