Hypersurfaces With Constant Mean Curvature in Spheres

Hilário Alencar and Manfredo do Carmo
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Hilário Alencar: Universidade Federal de Alagoas, Departamento de Matemática
Manfredo do Carmo: Universidade Federal de Alagoas, Departamento de Matemática

A chapter in Manfredo P. do Carmo – Selected Papers, 2012, pp 341-347 from Springer

Abstract: Abstract Let $$M^n$$ be a compact hypersurface of a sphere with constant mean curvature H. We introduce a tensor $$\phi$$ related to H and to the second fundamental form, and show that if $$|\phi|^2\leq B_{H}$$ , where $$B_{H}\neq 0$$ is a number depending only on H and n, then either $$|\phi|^2\equiv 0$$ or $$|\phi|^2\equiv{B}_{H}.$$ We also characterize all $$M^n$$ with $$|\phi|^2\equiv{B}_{H}.$$

Keywords: Constant mean curvature; spheres; minimal surfaces; totally umbilic; tori. (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-25588-5_25

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DOI: 10.1007/978-3-642-25588-5_25

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