The relative nullity of complex submanifolds and the Gauss map

The relative nullity of complex submanifolds and the Gauss map

We give a short and geometric proof, based on Jacobi fields, of a theorem of K. Abe that asserts that the relative index of nullity is trivial for complete non-totally geodesic complex projective submanifolds. Using this idea we prove a splitting theorem for complex Euclidean submanifolds with a non...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2016-04, Vol.144 (4), p.1689-1695
Hauptverfasser: Di Scala, Antonio J., Olmos, Carlos
Format: Artikel
Sprache:eng
Schlagworte:
D. GEOMETRY
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Zusammenfassung:We give a short and geometric proof, based on Jacobi fields, of a theorem of K. Abe that asserts that the relative index of nullity is trivial for complete non-totally geodesic complex projective submanifolds. Using this idea we prove a splitting theorem for complex Euclidean submanifolds with a non-trivial relative index of nullity.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/12987