Integral inequalities for closed linear Weingarten submanifolds in the product spaces

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 s...

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Bibliographic Details
Published in:Anais da Academia Brasileira de Ciências 2023-01, Vol.95 (3), p.e20230345-e20230345
Main Authors: SANTOS, FÁBIO R. DOS, SILVA, SYLVIA F. DA, SOUSA, ANTONIO F. DE
Format: Article
Language:English
Subjects:
Closed pnmc lw-submanifolds
MULTIDISCIPLINARY SCIENCES
product spaces
standard product
totally umbilical hypersurfaces
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Summary: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.
ISSN:0001-3765
1678-2690
1678-2690
DOI:10.1590/0001-3765202320230345