On Minimal Immersions with Parallel Normal Curvature Tensor

A. G. Colares and M. P. do Carmo
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A. G. Colares: Universidade Federal do Ceará, Departamento de Matemática
M. P. do Carmo: Instituto de Matemática Pura e Aplicada

A chapter in Manfredo P. do Carmo – Selected Papers, 2012, pp 129-138 from Springer

Abstract: Abstract In this paper we first prove the fo11owing theorem on reduction of codimension of minima1 immersions: Theorem 1 - Let x: Mn→X be a minima1 immersion of an n-dimensiona1 connected manifold Mn into an (n+l)-dimensiona1 space X of constant curvature. Assume that the curvature tensor of the norma1 connexion is paral1e1 in the norma1 bundle and the first norma1 space of the immersion has constant dimension k.

Keywords: Normal Space; Tangent Vector; Fundamental Form; Curvature Tensor; Constant Curvature (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-25588-5_11

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DOI: 10.1007/978-3-642-25588-5_11

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