Sur la Conjecture Des Tores Plats

Details Sur la Conjecture Des Tores Plats Sur la Conjecture Des Tores Plats

2002-02-25

arxiv.org/abs/math/0202257v1

Mathematics

Differential Geometry

Scientific paper

The present work is devoted to compact completely solvable solvmanifolds which admit Kahlerian metrics whose Kahler forms are homogeneous. In particular, we show that such manifolds are diffeomorphic to flat tori. Our proof is based on Dynkin diagrams associated to left invariant closed 2-forms in completely solvable Lie groups. These diagrams are shown to be closely related to Lagrangian foliations,primitive degrees of homogeneous spaces, and geometric structures such as $(\bkR^ n, Aff (\bkR^ n))$-structures on symplectic homogeneous spaces.

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