Kodai Mathematical Journal

Vanishing of homology groups, Ricci estimate for submanifolds and applications

Antonio Carlos Asperti and Ezio de Araújo Costa

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In this paper we obtain an estimate for the Ricci curvature and a criterion for the vanishing of the homology groups of compact submanifolds of spheres and Euclidean spaces. This criterion depends on the results of Lawson and Simons, Leung, and Xin on stable currents. As consequences we obtain a topological version of theorems of Cheng and Nakagawa, Alencar and do Carmo, and Xu, on hypersurfaces in spheres with constant mean curvature.

Article information

Kodai Math. J., Volume 24, Number 3 (2001), 313-328.

First available in Project Euclid: 19 January 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]


Asperti, Antonio Carlos; Costa, Ezio de Araújo. Vanishing of homology groups, Ricci estimate for submanifolds and applications. Kodai Math. J. 24 (2001), no. 3, 313--328. doi:10.2996/kmj/1106168806. https://projecteuclid.org/euclid.kmj/1106168806

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