Vanishing of homology groups, Ricci estimate for submanifolds and applications
Asperti, Antonio Carlos ; Costa, Ezio de Araújo
Kodai Math. J., Tome 24 (2001) no. 1, p. 313-328 / Harvested from Project Euclid
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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.
Publié le : 2001-05-14
Classification:  53C40,  53C42 
@article{1106168806,
     author = {Asperti, Antonio Carlos and Costa, Ezio de Ara\'ujo},
     title = {Vanishing of homology groups, Ricci estimate for submanifolds and applications},
     journal = {Kodai Math. J.},
     volume = {24},
     number = {1},
     year = {2001},
     pages = { 313-328},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1106168806}
}

Asperti, Antonio Carlos; Costa, Ezio de Araújo. Vanishing of homology groups, Ricci estimate for submanifolds and applications. Kodai Math. J., Tome 24 (2001) no. 1, pp.  313-328. http://gdmltest.u-ga.fr/item/1106168806/