PU BL IC Compact symplectic manifolds of low cohomogeneity ( corrected

This is a corrected version of my paper published in Journal of Geometry and Physics 25(1998), 205-226. I added missing cases to the classification theorem 1.1, namely the SO(n + 1)-manifold SO(n + 2)/(SO(n) × SO(2)), the SO(3)-manifold CP 2 and the SU(3)-manifold CP 1 × CP . Preface Christopher T. Woodward, in his review MR1619843 in MathSciNet, pointed out a gap in the classification of compact symplectic manifolds of cohomogeneity one in my paper [Le1998]. “Unfortunately, there is a mistake in (2.4). The author assumes that the map μ : M → △, where △ is the moment polytope, is smooth. This is not the case, for example, for M the product of two projective lines, and G=SU(2) acting diagonally. Therefore, his conclusions are only valid under this assumption.” The aim of this version is to correct that mistake and to find the missing cases in the previous classification. I also slightly improved the exposition of the previous version by adding a footnote, inserting few explanations, four new references (including the previous version of this paper), deleting some unimportant and imprecise remarks in the previous version and polishing few sentences. The main correction concerns the classification theorem 1.1. I have added Corollary 1, Lemma 2, Proposition 4, Lemma 5 and relations (E1), (E2), (E3), (E4), (E5), (E6) in the new version and modified the previous Proposition 2.3. In the revised version the previous formula (2.4) and Proposition 2.3 (now is Lemma 3) are applied only to special cases.