Four-dimensional compact solvmanifolds with and without complex analytic structures
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- January 2004
- DOI:
- 10.48550/arXiv.math/0401413
- arXiv:
- arXiv:math/0401413
- Bibcode:
- 2004math......1413H
- Keywords:
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- Mathematics - Complex Variables;
- Mathematics - Differential Geometry;
- Mathematics - Symplectic Geometry;
- 32Q55;
- 53C30;
- 14J80
- E-Print:
- 27 pages