A sharp integral inequality for compact Weingarten hypersurfaces under an Okumura type inequality

• Autorzy: Lima Eudes L. de , Lima Henrique F. de

Identyfikatory

DOI

10.4064/ba201228-2-2

• Języki publikacji: EN

Abstrakty

EN

Our aim in this paper is to provide a sharp integral inequality involving the norm of the traceless second fundamental form of a wide class of compact (without boundary) linear Weingarten hypersurfaces (including those with two distinct principal curvatures) immersed into a Riemannian space form. In particular, we generalize the results of Alías Meléndez (2020) when the ambient space form is the unit Euclidean sphere and give a new estimate when the space form is either the Euclidean space or the hyperbolic space. The sharpness of our integral inequality is realized by the totally umbilical spheres and, when the ambient space is the unit Euclidean sphere, by Clifford tori.

Słowa kluczowe

EN

Riemannian space forms; compact liner Weingarten hypersurfaces; Okumura type inequality; totally umbilical hypersurfaces; Clifford tori

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2021
• Tom: Vol. 69, no. 2
• Strony: 139--148
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Lima Eudes L. de

• Unidade Acadêmica de Ciências Exatas e da Natureza Universidade Federal de Campina Grande 58.900-000 Cajazeiras, Paraíba, Brazil

autor

Lima Henrique F. de

• Departamento de Matemática Universidade Federal de Campina Grande 58.429-970 Campina Grande, Paraíba, Brazil

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).