Splitting submanifolds of families of fake elliptic curves

Details Splitting submanifolds of families of fake elliptic curves Splitting submanifolds of families of fake elliptic curves

2010-03-08

arxiv.org/abs/1003.1583v1

Mathematics

Algebraic Geometry

15 pages

Scientific paper

Let N a compact complex submanifold of a compact complex manifold M. We say N splits in M, if the holomorphic tangent bundle sequence splits holomorphically. By a result of Mok a splitting submanifold of a Kaehler Einstein manifold with a projective structure is totally geodesic. The classification of all splitting submanifolds of families of fake elliptic curves given here completes the case of threefolds M with a projective structure by a previous result of the authors.

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