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

Márcio Henrique Batista da Silva^{[1]}

- [1] Universidade Federal de Alagoas Instituto de Matemática CEP: 57072-900 Maceió - Alagoas (Brazil)

Annales de l’institut Fourier (2011)

- Volume: 61, Issue: 4, page 1299-1322
- ISSN: 0373-0956

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topBatista 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 -

## References

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