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Conformally Flat Spaces of Codimension 2 in a Euclidean Space

Published online by Cambridge University Press:  20 November 2018

Bang-Yen Chen  and
Kentaro Yano
Bang-Yen Chen
Affiliation:
Michigan State University, East Lansing, Michigan
Kentaro Yano
Affiliation:
Michigan State University, East Lansing, Michigan
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In a previous paper [1], the authors introduced and studied the notion of special conformally flat spaces and quasi-umbilical hypersurfaces. In that paper, the authors proved that every conformally flat space of codimension one in a Euclidean space is special and, conversely, every special conformally flat space can be isometrically immersed in a Euclidean space as a quasi-umbilical hypersurface.

In the present paper, the authors study the conformally flat spaces of codimension 2 in a Euclidean space. (Manifolds, mappings, functions, etc. are assumed to be sufficiently differentiate and we shall restrict ourselves only to manifolds of dimension n > 3.)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 6 , December 1973 , pp. 1170 - 1173
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Chen, Bang-yen and Yano, Kentaro, Special conformally flat spaces and canal hyper surf ace, Tôhoku Math. J. 25 (1973), 177–184.Google Scholar
2. Yano, Kentaro and Shigeru, Ishihara, Pseudo-umbilical submanijolds of codimension 2, Kōdai Math. Sem. Rep. 21 (1969), 365–382.Google Scholar