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.
|Titolo:||Reducibility of complex submanifolds of the complex euclidean spaces|
|Data di pubblicazione:||2000|
|Digital Object Identifier (DOI):||10.1007/s002090000139|
|Appare nelle tipologie:||1.1 Articolo in rivista|