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AN EXTENSION OF THE CLASSICAL RIBAUCOUR TRANSFORMATION

Published online by Cambridge University Press:  09 July 2002

MARCOS DAJCZER  and
RUY TOJEIRO
MARCOS DAJCZER
Affiliation:
IMPA, Estrada Dona Castorina, 110, 22460-320 Rio de Janeiro, Brazil. marcos@impa.br
RUY TOJEIRO
Affiliation:
Universidade Federal de São Carlos, 13565-905 São Carlos, Brazil. tojeiro@dm.ufscar.br
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Abstract

We extend the notion of Ribaucour transformation from classical surface theory to the theory of holonomic submanifolds of pseudo-Riemannian space forms with arbitrary dimension and codimension, that is, submanifolds with flat normal bundle admitting a global system of principal coordinates. Bianchi gave a positive answer to the question of whether among the Ribaucour transforms of a surface with constant mean or Gaussian curvature there exist other surfaces with the same property. Our main achievement is to solve the same problem for the class of holonomic submanifolds with constant sectional curvature.

2000 Mathematical Subject Classification: 53B25, 58J72.

Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 85 , Issue 1 , March 2002 , pp. 211 - 232
Copyright
2002 London Mathematical Society

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