A note on toric contact geometry

[摘要] After observing that the well-known convexity theorems of symplectic geometry also hold for compact contact manifolds with an effective torus action whose Reeb vector field corresponds to an element of the Lie algebra of the torus, we use this fact together with a recent symplectic orbifold version of Delzant's theorem due to Lerman and Tolman [E. Lerman, S. Tolman, Trans. Am. Math. Sec. 349 (10) (1997) 4201-4230] to show that every such compact toric contact manifold can be obtained by a contact reduction from an odd dimensional sphere. (C) 2000 Elsevier Science B.V. All rights reserved.

[发布日期] 2000-10-01

[关键词] Lie algebra;Reeb vector field;symplectic geometry;moment map;polytope