1,720,976 research outputs found
On the geometry of almost contact metric manifolds of Kenmotsu type
No full textWe 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, , 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
A classification of certain almost alpha-Kenmotsu manifolds
No full textWe 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
On the structure and symmetry properties of almost S-manifolds
No full textWe prove that any simply connected S-manifold of CR-codimension is noncompact by showing that the complete, simply connected S-manifolds are all the CR products NxR^{s-1} with N Sasakian, endowed with a suitable product metric. N is a Sasakian φ-symmetric space if and only if M is CR-symmetric. The locally CR-symmetric S-manifolds are characterized by where is the Tanaka-Webster connection. This characterization is showed to be nonvalid for nonnormal almost S-manifolds
Levi-parallel contact Riemannian manifolds
No full textWe study the Riemannian geometry of contact manifolds with respect to a fixed admissible metric, making the Reeb vector field unitary and orthogonal to the contact distribution, under the assumption that the Levi-Tanaka form is parallel with respect to a canonical connection with torsion
A classification of spherical symmetric CR manifolds
No full textIn this paper we get different characterizations of the spherical strictly pseudoconvex CR manifolds admitting a CR-symmetric Webster metric by means of the Tanaka-Webster connection and of the Riemannian curvature tensor. As a consequence we obtain the classification of the simply connected, spherical symmetric pseudo-Hermitian manifolds
Some Einstein nilmanifolds with skew torsion arising in CR geometry
No full textWe describe some new examples of nilmanifolds admitting an Einstein with skew torsion invariant Riemannian metric. These are affine CR quadrics, whose CR structure is preserved by the characteristic connection
Almost Kenmotsu manifolds and local symmetry
No full textWe 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 with a condition of eta-parallelism
No full textWe consider almost Kenmotsu manifolds (M^{2n+1}, phi, xi, eta, g) with eta-parallel tensor h' = h o phi, 2h being the Lie derivative of the structure tensor phi with respect to the Reeb vector field xi. We describe the Riemannian geometry of an integral submanifold of the distribution orthogonal to xi, characterizing the CR-integrability of the structure. Under the additional condition nabla_xi h'=0, the almost Kenmotsu manifold is locally a warped product. Finally, some lightlike structures on M^{2n+1} are introduced and studied
Some paracontact metric structures on contact metric manifolds
No full textWe consider contact metric manifolds such that the Jacobi operator anticommutes with the structure tensor field . These manifolds admit two paracontact metric structures compatible with the contact form . We describe some geometric properties of these structures
Almost Kenmotsu manifolds and nullity distributions
No full textWe characterize almost contact metric manifolds which are CR-integrable almost Kenmotsu, through the existence of a suitable linear connection. We classify almost Kenmotsu manifolds satisfying a certain nullity condition, we give examples and completely describe the three dimensional case
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