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October, 2004 Foliated CR manifolds
J. Math. Soc. Japan 56(4): 1031-1068 (October, 2004). DOI: 10.2969/jmsj/1190905448


We study foliations on CR manifolds and show the following. (1) For a strictly pseudoconvex CR manifold M, the relationship between a foliation F on M and its pullback π*F on the total space C(M) of the canonical circle bundle of M is given, with emphasis on their interrelation with the Webster metric on M and the Fefferman metric on C(M), respectively. (2) With a tangentially CR foliation F on a nondegenerate CR manifold M, we associate the basic Kohn-Rossi cohomology of (M,F) and prove that it gives the basis of the E2-term of the spectral sequence naturally associated to F. (3) For a strictly pseudoconvex domain Ω in a complex Euclidean space and a foliation F defined by the level sets of the defining function of Ω on a neighborhood U of Ω, we give a new axiomatic description of the Graham-Lee connection, a linear connection on U which induces the Tanaka-Webster connection on each leaf of F. (4) For a foliation F on a nondegenerate CR manifold M, we build a pseudohermitian analogue to the theory of the second fundamental form of a foliation on a Riemannian manifold, and apply it to the flows obtained by integrating infinitesimal pseudohermitian transformations on M.


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Sorin DRAGOMIR. Seiki NISHIKAWA. "Foliated CR manifolds." J. Math. Soc. Japan 56 (4) 1031 - 1068, October, 2004.


Published: October, 2004
First available in Project Euclid: 27 September 2007

zbMATH: 1066.53059
MathSciNet: MR2091416
Digital Object Identifier: 10.2969/jmsj/1190905448

Primary: 53C12
Secondary: 32V05 , 32V40 , 53C50

Keywords: basic Kohn-Rossi cohomology , Fefferman metric , Graham-Lee connection , infinitesimal pseudohermitian transformation , Tanaka-Webster connection , tangentially CR foliation

Rights: Copyright © 2004 Mathematical Society of Japan


Vol.56 • No. 4 • October, 2004
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