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