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An Extension of The Classical Ribaucour Transformation
Author(s) -
Dajczer Marcos,
Tojeiro Ruy
Publication year - 2002
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/85.1.211
Subject(s) - mathematics , pure mathematics , gaussian curvature , extension (predicate logic) , transformation (genetics) , mean curvature , surface (topology) , constant curvature , constant (computer programming) , codimension , class (philosophy) , space (punctuation) , mathematical analysis , holonomic , curvature , geometry , biochemistry , chemistry , computer science , gene , programming language , linguistics , philosophy , physics , quantum mechanics , artificial intelligence
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.