8 research outputs found
Anti-Invariant Riemannian Submersions from Cosymplectic Manifolds
We introduce anti-invariant Riemannian submersions from cosymplectic
manifolds onto Riemannian manifolds. We survey main results of anti-invariant
Riemannian submersions defined on cosymplectic manifolds. We investigate
necessary and sufficient condition for an anti-invariant Riemannian submersion
to be totally geodesic and harmonic. We give examples of anti-invariant
submersions such that characteristic vector field {\xi} is vertical or
horizontal. Moreover we give decomposition theorems by using the existence of
anti-invariant Riemannian submersions.Comment: arXiv admin note: text overlap with arXiv:1006.0081, arXiv:1006.0076,
arXiv:1302.4906 by other author
Nullity conditions in paracontact geometry
The paper is a complete study of paracontact metric manifolds for which the
Reeb vector field of the underlying contact structure satisfies a nullity
condition (the condition \eqref{paranullity} below, for some real numbers and ). This class of pseudo-Riemannian manifolds,
which includes para-Sasakian manifolds, was recently defined in \cite{MOTE}. In
this paper we show in fact that there is a kind of duality between those
manifolds and contact metric -spaces. In particular, we prove
that, under some natural assumption, any such paracontact metric manifold
admits a compatible contact metric -structure (eventually
Sasakian). Moreover, we prove that the nullity condition is invariant under -homothetic deformations and determines the whole curvature tensor
field completely. Finally non-trivial examples in any dimension are presented
and the many differences with the contact metric case, due to the non-positive
definiteness of the metric, are discussed.Comment: Different. Geom. Appl. (to appear