We consider locally symmetric almost Kenmotsu manifolds showing that such a manifold is a Kenmotsu manifold if and only if the Lie derivative of the structure, with respect to the Reeb vector field xi, vanishes. Furthermore, assuming that for a (2n+1)-dimensional locally symmetric almost Kenmotsu manifold such Lie derivative does not vanish and the curvature satisfies R_{XY}xi = 0 for any X,Y orthogonal to xi, we prove that the manifold is locally isometric to the Riemannian product of an (n+1)-dimensional manifold of constant curvature -4 and a flat n-dimensional manifold. We give an example of such a manifold.
Almost Kenmotsu manifolds and local symmetry
DILEO, GIULIA;PASTORE, Anna Maria
2007-01-01
Abstract
We consider locally symmetric almost Kenmotsu manifolds showing that such a manifold is a Kenmotsu manifold if and only if the Lie derivative of the structure, with respect to the Reeb vector field xi, vanishes. Furthermore, assuming that for a (2n+1)-dimensional locally symmetric almost Kenmotsu manifold such Lie derivative does not vanish and the curvature satisfies R_{XY}xi = 0 for any X,Y orthogonal to xi, we prove that the manifold is locally isometric to the Riemannian product of an (n+1)-dimensional manifold of constant curvature -4 and a flat n-dimensional manifold. We give an example of such a manifold.File in questo prodotto:
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