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Conformal Geometry and the Cyclides of Dupin

Published online by Cambridge University Press:  20 November 2018

Thomas E. Cecil  and
Patrick J. Ryan
Thomas E. Cecil
Affiliation:
College of the Holy Cross, Worcester, Massachusetts
Patrick J. Ryan
Affiliation:
Indiana University at South Bend, South Bend, Indiana
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A Riemannian manifold (M, g) is said to be conformally flat if every point has a neighborhood conformai to an open set in Euclidean space. Over the past thirty years, many papers have appeared attacking, with varying degrees of success, the problem of classifying the conformally flat spaces which occur as hypersurfaces in Euclidean space. Most of these start from the following pointwise result of Schouten.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 4 , April 1980 , pp. 767 - 782
Copyright
Copyright © Canadian Mathematical Society 1980

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