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Intrinsic
obstructions to the existence of isometric minimal
immersions
Theodoros Vlachos |
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Vol. 205 (2002), No. 2, 491–510
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Abstract |
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S.S. Chern raised the problem to find necessary and sufficient conditions for a given Riemannian manifold to be realizable on a minimal submanifold of a Euclidean space. The aim of this paper is to provide new necessary conditions. For minimal submanifolds in a Euclidean space we consider the negative of the Ricci tensor as defining a new metric, which is nothing but the third fundamental form, and seek curvature properties of this metric. |
Milestones
Received: 16 November 2000
Published: 1 August 2002
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Authors |
| Theodoros Vlachos | |
| Department of Mathematics University of Ioannina Ioannina 45110, Greece |
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