We analyse in a systematic way the four dimensionnal Einstein-Weyl spaces equipped with a diagonal Kähler Bianchi IX metric. In particular, we show that the subclass of EinsteinWeyl structures with a constant conformal scalar curvature is the one with a conformally scalar flat but not necessarily scalar flat metric ; we exhibit its 3-parameter distance and Weyl one-form. This extends previous a...

The peeling theorem of general relativity predicts that the Weyl curvature scalars Ψn (n = 0, . . . , 4), when constructed from a suitable null tetrad in an asymptotically flat spacetime, fall off asymptotically as rn−5 along outgoing radial null geodesics. This leads to the interpretation of Ψ4 as outgoing gravitational radiation at large distances from the source. We have performed numerical ...

‎The object of the present paper is to introduce and study a type of non-flat semi-Riemannian manifolds‎, ‎called‎, ‎super generalized recurrent manifolds which generalizes both the notion of hyper generalized recurrent manifolds [‎A.A‎. ‎Shaikh and A‎. ‎Patra‎, On a generalized class of recurrent manifolds‎, Arch‎. ‎Math‎. ‎(Brno) 46 (2010) 71--78‎.] and weakly generalized recurrent manifolds ...

The condition for the vanishing of the Weyl tensor is integrated in the spherically symmetric case. Then, the resulting expression is used to find new, conformally flat, interior solutions to Einstein equations for locally anisotropic fluids. The slow evolution of these models is contrasted with the evolution of models with similar energy density or radial pressure distribution but non-vanishin...

We analyse in a systematic way the (non-)compact n-dimensional Einstein-Weyl spaces equipped with a cohomogeneity-one metric. In that context, with no compactness hypothesis for the manifold on which lives the Einstein-Weyl structure, we prove that, as soon as the (n-1)-dimensional basis space is an homogeneous reductive Riemannian space with an unimodular group of left-acting isometries G : • ...

We construct a new class of scalar noncommutative multi-solitons on an arbitrary Kähler manifold by using Berezin’s geometric approach to quantization and its generalization to deformation quantization. We analyze the stability condition which arises from the leading 1/h̄ correction to the soliton energy and for homogeneous Kähler manifolds obtain that the stable solitons are given in terms of g...

Consider a complex symplectic manifold X and the algebroid stack WX of deformation-quantization. For two regular holonomic WXmodules Li (i = 0, 1) supported by smooth Lagrangian submanifolds, we prove that the complex RHom WX (L1,L0) is perverse over the field Wpt and dual to the complex RHomWX(L0,L1).

We analyse in a systematic way the (non-)compact n-dimensional Einstein-Weyl spaces equipped with a cohomogeneity-one metric. In that context, with no compactness hypothesis for the manifold on which lives the Einstein-Weyl structure, we prove that, as soon as the (n-1)-dimensional space is a homogeneous reductive Riemannian space with a unimodular group of left-acting isometries G : • there ex...

In [23] a nice looking formula is conjectured for a deformed product of functions on a symplectic manifold in case it concerns a hermitian symmetric space of non-compact type. We derive such a formula for simply connected symmetric symplectic spaces using ideas from geometric quantization and prequantization of symplectic groupoids. We compute the result explicitly for the natural 2-dimensional...