We study D-homothetic deformations of almost alpha-Kenmotsu structures. We characterize almost contact metric manifolds which are CR-integrable almost alpha-Kenmotsu manifolds, through the existence of a canonical linear connection, invariant under D-homothetic deformations. If the canonical connection associated to the structure (phi, xi, eta, g) has parallel torsion and curvature, then the local geometry is completely determined by the dimension of the manifold and the spectrum of the operator h' defined by 2 alpha h' = (L xi phi) o phi. In particular, the manifold is locally equivalent to a Lie group endowed with a left invariant almost alpha-Kenmotsu structure. In the case of almost a-Kenmotsu (k, mu)'-spaces, this classification gives rise to a scalar invariant depending on the real numbers K and alpha.
A classification of certain almost alpha-Kenmotsu manifolds
DILEO, GIULIA
2011-01-01
Abstract
We study D-homothetic deformations of almost alpha-Kenmotsu structures. We characterize almost contact metric manifolds which are CR-integrable almost alpha-Kenmotsu manifolds, through the existence of a canonical linear connection, invariant under D-homothetic deformations. If the canonical connection associated to the structure (phi, xi, eta, g) has parallel torsion and curvature, then the local geometry is completely determined by the dimension of the manifold and the spectrum of the operator h' defined by 2 alpha h' = (L xi phi) o phi. In particular, the manifold is locally equivalent to a Lie group endowed with a left invariant almost alpha-Kenmotsu structure. In the case of almost a-Kenmotsu (k, mu)'-spaces, this classification gives rise to a scalar invariant depending on the real numbers K and alpha.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
