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Submanifolds of codimension two attaining equality in an extrinsic inequality

Published online by Cambridge University Press:  01 March 2009

MARCOS DAJCZER  and
RUY TOJEIRO
MARCOS DAJCZER
Affiliation:
IMPA—Estrada Dona Castorina, 110 22460-320 Rio de Janeiro, Brazil. e-mail: [email protected]
RUY TOJEIRO
Affiliation:
Universidade Federal de São Carlos, 13565-905 São Carlos, Brazil. e-mail: [email protected]
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Abstract

We provide a parametric construction in terms of minimal surfaces of the Euclidean submanifolds of codimension two and arbitrary dimension that attain equality in an inequality due to De Smet, Dillen, Verstraelen and Vrancken. The latter involves the scalar curvature, the norm of the normal curvature tensor and the length of the mean curvature vector.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 2 , March 2009 , pp. 461 - 474
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

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