The Calabi-Yau equation on 4-manifolds over 2-tori

Details The Calabi-Yau equation on 4-manifolds over 2-tori The Calabi-Yau equation on 4-manifolds over 2-tori

2011-03-21

arxiv.org/abs/1103.3995v1

Mathematics

Differential Geometry

24 pages

Scientific paper

This paper pursues the study of the Calabi-Yau equation on certain symplectic non-Kaehler 4-manifolds, building on a key example of Tosatti-Weinkove in which more general theory had proved less effective. Symplectic 4-manifolds admitting a 2-torus fibration over a 2-torus base are modelled on one of three solvable Lie groups. Having assigned an invariant almost-Kaehler structure and a volume form that effectively varies only on the base, one seeks a symplectic form with this volume. Our approach simplifies the previous analysis of the problem, and establishes the existence of solutions in various other cases.

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