A characterization of submanifolds of extrinsic symmetric spaces

A characterization of submanifolds of extrinsic symmetric spaces

A submanifold M ⊂ R n lies in the sphere S n − 1 iff it carries a parallel umbilic normal vector field. We extend this theorem by replacing the sphere S n − 1 by an arbitrary extrinsic symmetric space S ⊂ R n .

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Veröffentlicht in:Differential geometry and its applications 2010-06, Vol.28 (3), p.355-358
Hauptverfasser: Eschenburg, J., Tribuzy, R.
Format: Artikel
Sprache:eng
Schlagworte:
Connections
Differential geometry
Gauss equations
Mathematical analysis
Mathematics
Theorems
Vector subbundles
Vectors (mathematics)
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Zusammenfassung:A submanifold M ⊂ R n lies in the sphere S n − 1 iff it carries a parallel umbilic normal vector field. We extend this theorem by replacing the sphere S n − 1 by an arbitrary extrinsic symmetric space S ⊂ R n .
ISSN:0926-2245
1872-6984
DOI:10.1016/j.difgeo.2010.01.002