Minimal Immersions of Kahler manifolds into Euclidean Spaces

It is proved here that a minimal isometric immersion of a Kähler-Einstein or homogeneous Kähler-manifold into an Euclidean space must be totally geodesic

On an assertion in Riemann's Habilitationvortrag

We study an assertion in Riemann's Habilitation Lecture of 1854. Namely, the determination of the metric given $n\frac{n-1}{2}$ sectional curvatures. We give several counterexamples to a Riemann's clai

Reducibility of complex submanifolds of the complex euclidean spaces

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

Autoparallel distributions and splitting theorems

We study some links between autoparallel distributions and the factorization of a riemannian manifold. Finally, we prove a splitting theorem for Lie groups with biinvariant metric

On submanifolds whose shape operator is unipotent

The object of this article is to characterize submanifolds of the Euclidean space whose shape operator is unipoten

Kahler immersions of the disc into polydiscs

We give a concrete example of non totally geodesic Kahler immersion of a disc into a polydis

Minimal homogeneous submanifolds in euclidean spaces

We prove that minimal (extrinsically) homogeneous submanifolds of the Euclidean space are totally geodesic. As an application, we obtain that a complex (intrisecally) homogeneous submanifold of a complex Euclidean space must be totally geodesic