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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)].

MSC:
53C30 Differential geometry of homogeneous manifolds
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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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
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