Simons Type Equation in ${𝕊}^2\times ℝ$ and ${ℍ}^2\times ℝ$ and Applications

Batista da Silva, Márcio Henrique. "Simons Type Equation in $\mathbb{S}^{2}\times \mathbb{R}$ and $\mathbb{H}^2\times \mathbb{R}$ and Applications." Annales de l’institut Fourier 61.4 (2011): 1299-1322. <http://eudml.org/doc/219743>.

@article{BatistadaSilva2011,
abstract = {Let $\Sigma ^2$ be an immersed surface in $M^2(c)\times \mathbb\{R\}$ with constant mean curvature. We consider the traceless Weingarten operator $\phi $ associated to the second fundamental form of the surface, and we introduce a tensor $S$, related to the Abresch-Rosenberg quadratic differential form. We establish equations of Simons type for both $\phi $ and $S$. By using these equations, we characterize some immersions for which $|\phi |$ or $|S|$ is appropriately bounded.},
affiliation = {Universidade Federal de Alagoas Instituto de Matemática CEP: 57072-900 Maceió - Alagoas (Brazil)},
author = {Batista da Silva, Márcio Henrique},
journal = {Annales de l’institut Fourier},
keywords = {Surface with constant mean curvature; Simons type equation; Codazzi’s equation; constant mean curvature; Abresch-Rosenberg differential form},
language = {eng},
number = {4},
pages = {1299-1322},
publisher = {Association des Annales de l’institut Fourier},
title = {Simons Type Equation in $\mathbb\{S\}^\{2\}\times \mathbb\{R\}$ and $\mathbb\{H\}^2\times \mathbb\{R\}$ and Applications},
url = {http://eudml.org/doc/219743},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Batista da Silva, Márcio Henrique
TI - Simons Type Equation in $\mathbb{S}^{2}\times \mathbb{R}$ and $\mathbb{H}^2\times \mathbb{R}$ and Applications
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 4
SP - 1299
EP - 1322
AB - Let $\Sigma ^2$ be an immersed surface in $M^2(c)\times \mathbb{R}$ with constant mean curvature. We consider the traceless Weingarten operator $\phi $ associated to the second fundamental form of the surface, and we introduce a tensor $S$, related to the Abresch-Rosenberg quadratic differential form. We establish equations of Simons type for both $\phi $ and $S$. By using these equations, we characterize some immersions for which $|\phi |$ or $|S|$ is appropriately bounded.
LA - eng
KW - Surface with constant mean curvature; Simons type equation; Codazzi’s equation; constant mean curvature; Abresch-Rosenberg differential form
UR - http://eudml.org/doc/219743
ER -