Open Access
2014 Submanifolds with nonparallel first normal bundle revisited
Marcos Dajczer, Ruy Tojeiro
Publ. Mat. 58(1): 179-191 (2014).


In this paper, we analyze the geometric structure of a Euclidean submanifold whose osculating spaces form a nonconstant family of proper subspaces of the same dimension. We prove that if the rate of change of the osculating spaces is small, then the submanifold must be a (submanifold of a) ruled submanifold of a very special type. We also give a sharp estimate of the dimension of the rulings.


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Marcos Dajczer. Ruy Tojeiro. "Submanifolds with nonparallel first normal bundle revisited." Publ. Mat. 58 (1) 179 - 191, 2014.


Published: 2014
First available in Project Euclid: 20 December 2013

zbMATH: 1290.53006
MathSciNet: MR3161513

Primary: 53B25

Keywords: Euclidean submanifold , first normal bundle

Rights: Copyright © 2014 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.58 • No. 1 • 2014
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