Abstract
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.
Citation
Antonio Carlos Asperti. Ezio de Araújo Costa. "Vanishing of homology groups, Ricci estimate for submanifolds and applications." Kodai Math. J. 24 (3) 313 - 328, 2001. https://doi.org/10.2996/kmj/1106168806
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