A sharp integral inequality for compact Weingarten hypersurfaces under an Okumura type inequality. (English) Zbl 1494.53052
In this paper, the authors provides a sharp integral inequality that involves the traceless second fundamental form of a compact linear Weingarten hypersurface immersed in a Riemannian space form. They show when equality occurs in this inequality, the hypersurface must be a totally umbilical sphere or a Clifford torus.
Reviewer: Georges Habib (Beirut)
MSC:
| 53C24 | Rigidity results |
| 53C40 | Global submanifolds |
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
Keywords:
Clifford tori; Riemannian space forms; totally umbilical hypersurfaces; Okumura-type inequality; compact linear Weingarten hypersurfacesReferences:
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| [21] | Cajazeiras, Paraíba, Brazil E-mail: eudes.leite@professor.ufcg.edu.br |
| [22] | Henrique F. de Lima |
| [23] | Campina Grande, Paraíba, Brazil E-mail: henrique@mat.ufcg.edu.br |
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