Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 56, Number 4 (2004), 1031-1068.
Foliated CR manifolds
We study foliations on CR manifolds and show the following. (1) For a strictly pseudoconvex CR manifold , the relationship between a foliation on and its pullback on the total space of the canonical circle bundle of is given, with emphasis on their interrelation with the Webster metric on and the Fefferman metric on , respectively. (2) With a tangentially CR foliation on a nondegenerate CR manifold , we associate the basic Kohn-Rossi cohomology of and prove that it gives the basis of the -term of the spectral sequence naturally associated to . (3) For a strictly pseudoconvex domain in a complex Euclidean space and a foliation defined by the level sets of the defining function of on a neighborhood of , we give a new axiomatic description of the Graham-Lee connection, a linear connection on which induces the Tanaka-Webster connection on each leaf of . (4) For a foliation on a nondegenerate CR manifold , 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 .
J. Math. Soc. Japan, Volume 56, Number 4 (2004), 1031-1068.
First available in Project Euclid: 27 September 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53C12: Foliations (differential geometric aspects) [See also 57R30, 57R32]
Secondary: 32V05: CR structures, CR operators, and generalizations 32V40: Real submanifolds in complex manifolds 53C50: Lorentz manifolds, manifolds with indefinite metrics
DRAGOMIR, Sorin; NISHIKAWA, Seiki. Foliated CR manifolds. J. Math. Soc. Japan 56 (2004), no. 4, 1031--1068. doi:10.2969/jmsj/1190905448. https://projecteuclid.org/euclid.jmsj/1190905448