Four-dimensional compact solvmanifolds with and without complex analytic structures

Details Four-dimensional compact solvmanifolds with and without complex analytic structures Four-dimensional compact solvmanifolds with and without complex analytic structures

2004-01-29

arxiv.org/abs/math/0401413v1

Complex and Kaehler structures on compact solvmanifolds, J. Symplectic Geom., Vol. 3, No. 4, 2005.

Mathematics

Complex Variables

27 pages

Scientific paper

We classify four-dimensional compact solvmanifolds up to diffeomorphism, while determining which of them have complex analytic structures. In particular, we shall see that a four-dimensional compact solvmanifold S can be written, up to double covering, as G/L where G is a simply connected solvable Lie group and L is a lattice of G, and every complex structure J on S is the canonical complex structure induced from a left-invariant complex structure on G. We also give a complete list of all the complex structures on four-dimensional compact homogeneous spaces, referring to their corresponding complex surfaces.

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