2023
DOI: 10.1590/0001-3765202320230345
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Integral inequalities for closed linear Weingarten submanifolds in the product spaces

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

Abstract: An integral inequality for closed linear Weingarten π‘š-submanifolds with parallel normalized mean curvature vector field (pnmc lw-submanifolds) in the product spaces 𝑀 𝑛 (𝑐) Γ— ℝ, 𝑛 > π‘š β‰₯ 4, where 𝑀 𝑛 (𝑐) is a space form of constant sectional curvature 𝑐 ∈ {βˆ’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 π•Š 1 (√1 βˆ’ π‘Ÿ 2 ) Γ— π•Š π‘šβˆ’1 (π‘Ÿ) with 0 < π‘Ÿ < 1 when 𝑐 … Show more

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