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The normal curvature of totally real submanifolds of S6(1)

Published online by Cambridge University Press:  18 May 2009

P. J. De Smet ,
F. Dillen ,
L. Verstraelen  and
L. Vrancken
P. J. De Smet
Affiliation:
Katholieke Universiteit Leuven, Departement Wiskunde, Celestijnenlaan 200 B, B-3001 Leuven, Belgium
F. Dillen
Affiliation:
Katholieke Universiteit Leuven, Departement Wiskunde, Celestijnenlaan 200 B, B-3001 Leuven, Belgium
L. Verstraelen
Affiliation:
Katholieke Universiteit Leuven, Departement Wiskunde, Celestijnenlaan 200 B, B-3001 Leuven, Belgium
L. Vrancken
Affiliation:
Katholieke Universiteit Leuven, Departement Wiskunde, Celestijnenlaan 200 B, B-3001 Leuven, Belgium
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Abstract

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We prove the pointwise inequality 0 ≥ ρ + ρ⊥ – 1 involving the normalized scalar curvature ρ and normal scalar curvature ρ⊥ of a totally real 3-dimensional submanifold of the nearly Kaehler 6-sphere. Further we classify submanifolds realizing the equality in this inequality.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 2 , May 1998 , pp. 199 - 204
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

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