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2004•Taiwanese Journal of MathematicsOpen access

CONFORMALLY FLAT HYPERSURFACES IN REAL SPACE FORMS WITH LEAST TENSION

Bang‐Yen Chen, Franki Dillen, Johan Fastenakels, Leopold Verstraelen

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Abstract

Roughly speaking, an ideal immersion of a Riemannian manifold into a real space form is an isometric immersion which receives the least possible amount of tension imposed on the submanifold from the ambient space. The purpose of this paper is to classify conformally flat ideal hypersurfaces in real space forms; thus we completely determine conformally flat manifolds which admit codimension one isometric immersions into real space forms with least possible tension.

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Roughly speaking, an ideal immersion of a Riemannian manifold into a real space form is an isometric immersion which receives the least possible amount of tension imposed on the submanifold from the ambient space. The purpose of this paper is to classify conformally flat ideal hypersurfaces in real space forms; thus we completely determine conformally flat manifolds which admit codimension one isometric immersions into real space forms with least possible tension.

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Available abstract

Roughly speaking, an ideal immersion of a Riemannian manifold into a real space form is an isometric immersion which receives the least possible amount of tension imposed on the submanifold from the ambient space. The purpose of this paper is to classify conformally flat ideal hypersurfaces in real space forms; thus we completely determine conformally flat manifolds which admit codimension one isometric immersions into real space forms with least possible tension.

Key concepts: Space form, Mathematics, Immersion (mathematics), Codimension, Submanifold, Ambient space, Isometric exercise, Pure mathematics

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