Archivio Istituzionale della RicercaLet M be a simply connected complex submanifold of CN. We prove that M is irreducible, up a totally geodesic factor,if and only if the normal holonomy group acts irreducibly. This is an extrinsic analogue of the well-known De Rham decomposition theorem for a complex manifold. Our result is not valid in the real context, as it is shown by many counterexamples.
Reducibility of complex submanifolds of the complex euclidean spaces / DI SCALA, ANTONIO JOSE'. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - STAMPA. - 235:(2000), pp. 251-257. [10.1007/s002090000139]
Reducibility of complex submanifolds of the complex euclidean spaces
DI SCALA, ANTONIO JOSE'
2000
Abstract
Let M be a simply connected complex submanifold of CN. We prove that M is irreducible, up a totally geodesic factor,if and only if the normal holonomy group acts irreducibly. This is an extrinsic analogue of the well-known De Rham decomposition theorem for a complex manifold. Our result is not valid in the real context, as it is shown by many counterexamples.
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https://hdl.handle.net/11583/1660756
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