399 research outputs found
3-Sasakian manifolds, 3-cosymplectic manifolds and Darboux theorem
We present a compared analysis of some properties of 3-Sasakian and
3-cosymplectic manifolds. We construct a canonical connection on an almost
3-contact metric manifold which generalises the Tanaka-Webster connection of a
contact metric manifold and we use this connection to show that a 3-Sasakian
manifold does not admit any Darboux-like coordinate system. Moreover, we prove
that any 3-cosymplectic manifold is Ricci-flat and admits a Darboux coordinate
system if and only it is flat.Comment: 14 pages, LaTeX; some minor misprints correcte
Curvature properties of 3-quasi-Sasakian manifolds
We find some curvature properties of 3-quasi-Sasakian manifolds which are
similar to some well-known identities holding in the Sasakian case. As an
application, we prove that any 3-quasi-Sasakian manifold of constant horizontal
sectional curvature is necessarily either 3-\alpha-Sasakian or 3-cosymplectic.Comment: 7 pages, to appear in Int. J. Geom. Methods Mod. Phys. (IJGMMP
Some remarks on cosymplectic 3-structures
In this note we briefly review some recent results of the authors on the
topological and geometrical properties of 3-cosymplectic manifolds.Comment: 6 page
Hard Lefschetz Theorem for Sasakian manifolds
We prove that on a compact Sasakian manifold of dimension
, for any the wedge product with
defines an isomorphism between the spaces of harmonic forms
and . Therefore it induces
an isomorphism between the de Rham cohomology spaces and
. Such isomorphism is proven to be independent of the choice of a
compatible Sasakian metric on a given contact manifold. As a consequence, an
obstruction for a contact manifold to admit Sasakian structures is found.Comment: 19 pages, 1 figure, accepted for publication in the Journal of
Differential Geometr
Cosymplectic p-spheres
We introduce cosymplectic circles and cosymplectic spheres, which are the
analogues in the cosymplectic setting of contact circles and contact spheres.
We provide a complete classification of compact 3-manifolds that admit a
cosymplectic circle. The properties of tautness and roundness for a
cosymplectic -sphere are studied. To any taut cosymplectic circle on a
three-dimensional manifold we are able to canonically associate a complex
structure and a conformal symplectic couple on . We prove
that a cosymplectic circle in dimension three is round if and only if it is
taut. On the other hand, we provide examples in higher dimensions of
cosymplectic circles which are taut but not round and examples of cosymplectic
circles which are round but not taut.Comment: 17 pages, accepted for publication in Journal of Geometry and Physic
Examples of compact K-contact manifolds with no Sasakian metric
Using the Hard Lefschetz Theorem for Sasakian manifolds, we find two examples
of compact K-contact nilmanifolds with no compatible Sasakian metric in
dimensions five and seven, respectivelyComment: 8 pages, accepted for publication in IJGMMP (Proceedings of the XXII
IFWGP, University of Evora, Portugal
A non-Sasakian Lefschetz K-contact manifold of Tievsky type
We find a family of five dimensional completely solvable compact manifolds
that constitute the first examples of -contact manifolds which satisfy the
Hard Lefschetz Theorem and have a model of Tievsky type just as Sasakian
manifolds but do not admit any Sasakian structure.Comment: 10 pages, to appear in Proceedings of the American Mathematical
Societ
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