We analyze the Riemannian geometry of almost alpha-Kenmotsu manifolds, focusing on local symmetries and on some vanishing conditions for the Riemannian curvature. If the characteristic vector field of an almost alpha-Kenmotsu structure belongs to the so-called (kappa,mu)'-nullity distribution, $\kappa < -\alpha^2$, then the Riemannian curvature is completely determined. These manifolds provide a special case of a wider class of almost alpha-Kenmotsu manifolds, for which an operator h' associated to the structure is eta-parallel and has constant eigenvalues. All these manifolds are locally warped products. Finally, we give a local classification of almost alpha-Kenmotsu manifolds, up to D-homothetic deformations. Under suitable conditions, they are locally isomorphic to Lie groups.
On the geometry of almost contact metric manifolds of Kenmotsu type
DILEO, GIULIA
2011-01-01
Abstract
We analyze the Riemannian geometry of almost alpha-Kenmotsu manifolds, focusing on local symmetries and on some vanishing conditions for the Riemannian curvature. If the characteristic vector field of an almost alpha-Kenmotsu structure belongs to the so-called (kappa,mu)'-nullity distribution, $\kappa < -\alpha^2$, then the Riemannian curvature is completely determined. These manifolds provide a special case of a wider class of almost alpha-Kenmotsu manifolds, for which an operator h' associated to the structure is eta-parallel and has constant eigenvalues. All these manifolds are locally warped products. Finally, we give a local classification of almost alpha-Kenmotsu manifolds, up to D-homothetic deformations. Under suitable conditions, they are locally isomorphic to Lie groups.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
