Reducibility of complex submanifolds of the complex euclidean space
نویسنده
چکیده
Let M be a simply connected complex submanifold of C . 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 counter-examples.
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