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Advances in Geometry

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Volume 18, Issue 4


On the umbilicity of generalized linear Weingarten hypersurfaces in hyperbolic spaces

Cícero P. Aquino / Márcio Batista / Henrique F. de Lima
  • Corresponding author
  • Departamento de Matemática, Universidade Federal de Campina Grande, 58429-970 Campina Grande, Paraíba, Brazil
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Published Online: 2018-03-26 | DOI: https://doi.org/10.1515/advgeom-2018-0005


We deal with complete generalized linear Weingarten hypersurfaces immersed in hyperbolic spaces. Under appropriate constraints on the image of the Gauss map, we present suitable conditions which guarantee the umbilicity of these hypersurfaces.

Keywords: Hyperbolic space; complete two-sided hypersurfaces; totally umbilical hypersurfaces; (r, s)-linear Weingarten hypersurfaces Gauss image

MSC 2010: Primary 53C42; Secondary 53B30; 53C24; 83C99


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About the article

Received: 2016-07-15

Published Online: 2018-03-26

Published in Print: 2018-10-25

Funding: The first author is partially supported by CNPq, Brazil, grant 302738/2014-2. The second author is partially supported by CNPq, Brazil, grant 456755/2014-4. The third author is partially supported by CNPq, Brazil, grant 303977/2015-9.

Citation Information: Advances in Geometry, Volume 18, Issue 4, Pages 425–430, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2018-0005.

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