The RICCI curvature of submanifolds and its applications

Author: Vlachos T.

Source: Quarterly Journal of Mathematics, Volume 55, Number 2, June 2004 , pp. 225-230(6)

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Abstract:

We prove the non-existence of stable currents or compact stable minimal submanifolds for a class of submanifolds in a Euclidean space which satisfies an operative condition involving the Ricci curvature. In addition, we prove that these submanifolds are homeomorphic to the sphere. Moreover, we give examples which show that our result is optimal.

Document Type: Research article

Affiliations: 1: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece

Publication date: 2004-06-01

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The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. Areas such as algebra, differential geometry, and global analysis receive particular emphasis. However the journal avoids specialization.