Four-dimensional compact solvmanifolds with and without complex analytic structures

Keizo Hasegawa

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arXiv · math/0401413

Four-dimensional compact solvmanifolds with and without complex analytic structures

Keizo Hasegawa

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Abstract

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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Keizo Hasegawa. 2004-01-29. Four-dimensional compact solvmanifolds with and without complex analytic structures. https://arxiv.org/abs/math/0401413

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