We define a generalized pseudohermitian structure on an almost CR manifold (M,HM,J) as a pair (h,P), where h is a positive definite fiber metric h on HM compatible with J, and P:TM-> TM is a smooth projector such that Im(P)=HM. We show that to each generalized pseudohermitian structure one can associate a canonical linear connection on the holomorphic bundle HM which is invariant under equivalence. This fact allows us to solve the equivalence problem in the case where HM is a kind 2 distribution. We study the curvature of the canonical connection, especially for the classes of standard homogeneous CR manifolds and 3-Sasakian manifolds. The basic formulas for isopseudohermitian immersions are also obtained in the attempt to enlarge the theory of pseudohermitian immersions between strongly pseudoconvex pseudohermitian manifolds of hypersurface type.
Generalized pseudohermitian manifolds
DILEO, GIULIA;LOTTA, Antonio
2012-01-01
Abstract
We define a generalized pseudohermitian structure on an almost CR manifold (M,HM,J) as a pair (h,P), where h is a positive definite fiber metric h on HM compatible with J, and P:TM-> TM is a smooth projector such that Im(P)=HM. We show that to each generalized pseudohermitian structure one can associate a canonical linear connection on the holomorphic bundle HM which is invariant under equivalence. This fact allows us to solve the equivalence problem in the case where HM is a kind 2 distribution. We study the curvature of the canonical connection, especially for the classes of standard homogeneous CR manifolds and 3-Sasakian manifolds. The basic formulas for isopseudohermitian immersions are also obtained in the attempt to enlarge the theory of pseudohermitian immersions between strongly pseudoconvex pseudohermitian manifolds of hypersurface type.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
