On a generalized Calabi-Yau equation
Dealing with the generalized Calabi-Yau equation proposed by Gromov on closed almost-Kähler manifolds, we extend to arbitrary dimension a non-existence result proved in complex dimension .
On a volume element of a Hitchin component
Let Σ be a closed oriented Riemann surface of genus at least 2. By using symplectic chain complex, we construct a volume element for a Hitchin component of Hom(π₁(Σ),PSLₙ(ℝ))/PSLₙ(ℝ) for n > 2.
On almost cosymplectic (−1, μ, 0)-spaces
In our previous paper, almost cosymplectic (κ, μ, ν)-spaces were defined as the almost cosymplectic manifolds whose structure tensor fields satisfy a certain special curvature condition. Amongst other results, it was proved there that any almost cosymplectic (κ, μ, ν)-space can be -homothetically deformed to an almost cosymplectic −1, μ′, 0)-space. In the present paper, a complete local description of almost cosymplectic (−1, μ, 0)-speces is established: “models” of such spaces are constructed,...
On almost cosymplectic manifolds with the structure vector field belonging to the -nullity distribution.
On almost cosymplectic (κ,μ,ν)-spaces
An almost cosymplectic (κ,μ,ν)-space is by definition an almost cosymplectic manifold whose structure tensor fields φ, ξ, η, g satisfy a certain special curvature condition (see formula (eq1b)). This condition is invariant with respect to the so-called -homothetic transformations of almost cosymplectic structures. For such manifolds, the tensor fields φ, h (), A ( = -∇ξ) fulfill a certain system of differential equations. It is proved that the leaves of the canonical foliation of an almost cosymplectic...
On alpha-Kenmotsu manifolds satisfying certain conditions.
On an inequality of Oprea for Lagrangian submanifolds
We show that a Lagrangian submanifold of a complex space form attaining equality in the inequality obtained by Oprea in [8], must be totally geodesic.
On Arnold's conjecture for symplectic fixed points
On category for cyclotomic rational Cherednik algebras
We study equivalences for category of the rational Cherednik algebras of type : a highest weight equivalence between and for and an action of on an explicit non-empty Zariski open set of parameters ; a derived equivalence between and whenever and have integral difference; a highest weight equivalence between and a parabolic category for the general linear group, under a non-rationality assumption on the parameter . As a consequence, we confirm special cases of conjectures...
On characterization of Poisson and Jacobi structures
We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson and Jacobi structures (canonical structures) associated with Lie algebroids and Jacobi algebroids.
On classical -matrices with parabolic carrier.
On conharmonic curvature tensor in -contact and Sasakian manifolds.
On connections, geodesics and sprays in synthetic differential geometry
On contact metric -harmonic manifolds.
On contact -spheres
We study invariant contact -spheres on principal circle-bundles and solve the corresponding existence problem in dimension 3. Moreover, we show that contact - spheres can only exist on -dimensional manifolds and we construct examples of contact -spheres on such manifolds. We also consider relations between tautness and roundness, a regularity property concerning the Reeb vector fields of the contact forms in a contact -sphere.
On curvature constructions of symplectic forms
We generalize the result of Lerman [Letters Math. Phys. 15 (1988)] concerning the condition of fatness of the canonical connection in a certain principal fibre bundle. We also describe new classes of symplectically fat bundles: twistor budles over spheres, bundles over quaternionic Kähler homogeneous spaces and locally homogeneous complex manifolds.
On F-algebroids and Dubrovin’s duality
In this note we introduce the concept of F-algebroid, and give its elementary properties and some examples. We provide a description of the almost duality for Frobenius manifolds, introduced by Dubrovin, in terms of a composition of two anchor maps of a unique cotangent F-algebroid.
On Hamiltonian-minimal Lagrangian tori in .
On Hopf algebra deformation approach to renormalization.
On Lagrange epimorphisms and Lagrange submersions.