Archivio Istituzionale della RicercaWe 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.
The relative nullity of complex submanifolds and the Gauss map / DI SCALA, ANTONIO JOSE'; Olmos, C.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 144:4(2016), pp. 1689-1695. [10.1090/proc/12987]
The relative nullity of complex submanifolds and the Gauss map
DI SCALA, ANTONIO JOSE';
2016
Abstract
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.
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https://hdl.handle.net/11583/2642194
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