Alekseevskij, D. V. Contact homogeneous spaces. (English. Russian original) Zbl 0721.53042 Funct. Anal. Appl. 24, No. 4, 324-325 (1990); translation from Funkts. Anal. Prilozh. 24, No. 4, 74-75 (1990). The present paper is devoted to the description of a simple construction of all contact homogeneous spaces \(M=G/H\) (where G is a Lie group) in terms of orbits of the co-adjoint representation of G. This construction is completely analogous to the construction of Kirillov-Kostant-Souriau for the symplectic homogeneous spaces [see, for example, V. Guillemin and S. Sternberg, Geometric asymptotics (1977; Zbl 0364.53011)]. Reviewer: E.D.Rodionov (Barnaul) Cited in 4 Documents MSC: 53C30 Differential geometry of homogeneous manifolds 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) Keywords:contact homogeneous spaces; Lie group; co-adjoint representation PDF BibTeX XML Cite \textit{D. V. Alekseevskij}, Funct. Anal. Appl. 24, No. 4, 324--325 (1990; Zbl 0721.53042); translation from Funkts. Anal. Prilozh. 24, No. 4, 74--75 (1990) Full Text: DOI References: [1] W. Guillemin and S. Sternberg, Geometric Asymptotics [Russian translation], Mir, Moscow (1981). [2] N. Hart, Geometric Quantization and Actions [Russian translation], Mir, Moscow (1985). [3] W. M. Boothby and H. C. Wang, Ann. Math.,68, 721-734 (1958). · Zbl 0084.39204 · doi:10.2307/1970165 [4] W. M. Boothby, Bull. Inst. Math. Acad. Sinica,8, No. 213, 341-351 (1980). [5] C. Le Brun, Math. Ann.,284, 353-376 (1989). · Zbl 0674.53036 · doi:10.1007/BF01442490 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.