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A Remark on the Reduction of Cauchy–Riemann Manifolds
Author(s) -
Loose Frank
Publication year - 2000
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200006)214:1<39::aid-mana39>3.0.co;2-9
Subject(s) - mathematics , hypersurface , pure mathematics , manifold (fluid mechanics) , cauchy–riemann equations , lie group , orbit (dynamics) , reduction (mathematics) , action (physics) , moment (physics) , moment map , group (periodic table) , mathematical analysis , geometry , symplectic geometry , mechanical engineering , physics , classical mechanics , quantum mechanics , engineering , aerospace engineering , chemistry , organic chemistry
The concept of a moment map for an action of a real Lie group by CR–diffeomorphisms on a CR–manifold M of hypersurface type is introduced. It gives rise to a natural reduction procedure in the sense that we construct a CR–structure on an associated orbit manifold M 0 for the case that the group acts freely and properly on M .