Integral inequalities for closed linear Weingarten submanifolds in the product spaces.
An Acad Bras Cienc
; 95(3): e20230345, 2023.
Article
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| MEDLINE
| ID: mdl-37909571
ABSTRACT
An integral inequality for closed linear Weingarten ð-submanifolds with parallel normalized mean curvature vector field (pnmc lw-submanifolds) in the product spaces ðð(ð) × â, ð > ð ≥ 4, where ðð(ð) is a space form of constant sectional curvature ð ∈ {-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 ð1(â1 - ð2) × ðð-1(ð) with 0 < ð < 1 when ð = 1. In the case where ð = -1, is obtained an integral inequality whose sharpness is attained only in the totally umbilical hypersurfaces. When ð = 2 and ð = 3, an integral inequality is also obtained with equality happening in the totally umbilical hypersurfaces.
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Colección:
01-internacional
Base de datos:
MEDLINE
Idioma:
En
Revista:
An Acad Bras Cienc
Año:
2023
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Article
País de afiliación:
Brasil