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Integral inequalities for closed linear Weingarten submanifolds in the product spaces

SANTOS, FÁBIO R. DOS ; SILVA, SYLVIA F. DA ; SOUSA, ANTONIO F. DE

Anais da Academia Brasileira de Ciências, 2023-01, Vol.95 (3), p.e20230345-e20230345 [Periódico revisado por pares]

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Título:
Integral inequalities for closed linear Weingarten submanifolds in the product spaces
Autor: SANTOS, FÁBIO R. DOS ; SILVA, SYLVIA F. DA ; SOUSA, ANTONIO F. DE
Assuntos: Closed pnmc lw-submanifolds ; MULTIDISCIPLINARY SCIENCES ; product spaces ; standard product ; totally umbilical hypersurfaces
É parte de: Anais da Academia Brasileira de Ciências, 2023-01, Vol.95 (3), p.e20230345-e20230345
Notas: ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
Descrição: An integral inequality for closed linear Weingarten -submanifolds with parallel normalized mean curvature vector field (pnmc lw-submanifolds) in the product spaces ( ) × ℝ, > ≥ 4, where ( ) is a space form of constant sectional curvature ∈ {-1, 1}, is proved. As an application is shown that the sharpness in this inequality is attained in the totally umbilical hypersurfaces, and in a certain family of standard product of the form 1(√1 - 2) × -1( ) with 0 < < 1 when = 1. In the case where = -1, is obtained an integral inequality whose sharpness is attained only in the totally umbilical hypersurfaces. When = 2 and = 3, an integral inequality is also obtained with equality happening in the totally umbilical hypersurfaces.
Editor: Academia Brasileira de Ciências
Idioma: Inglês;Português

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