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...

Using systematic calculations in spinor language, we obtain simple descriptions of the second order symmetry operators for the conformal wave equation, the Dirac-Weyl equation and the Maxwell equation on a curved four dimensional Lorentzian manifold. The conditions for existence of symmetry operators for the different equations are seen to be related. Computer algebra tools have been developed ...

In this paper we study the algebra L(Σ) generated by links in the manifold Σ¬[0, 1] where Σ is an oriented surface. This algebra has a filtration and the associated graded algebra L Gr (Σ) is naturally a Poisson algebra. There is a Poisson algebra homomorphism from the algebra ch (Σ) of chord diagrams on Σ to L Gr (Σ). We show that multiplication in L (Σ) provides a geometric way to define a de...

An algebraic curvature tensor is called Osserman if the eigenvalues of the associated Jacobi operator are constant on the unit sphere. A Riemannian manifold is called conformally Osserman if its Weyl conformal curvature tensor at every point is Osserman. We prove that a conformally Osserman manifold of dimension n 6= 3, 4, 16 is locally conformally equivalent either to a Euclidean space or to a...

A direct, bundle-theoretic method for defining and extending local isometries out of curvature data is developed. As a by-product, conceptual direct proofs of a classical result of Singer and a recent result of the authors are derived. A classical result of I. M. Singer [7] states that a Riemannian manifold is locally homogeneous if and only if its Riemannian curvature tensor together with its ...

We obtain a characterization of the Kerr metric among stationary, asymptotically flat, vacuum spacetimes, which extends the characterization in terms of the Simon tensor (defined only in the manifold of trajectories) to the whole spacetime. More precisely, we define a three index tensor on any spacetime with a Killing field, which vanishes identically for Kerr and which coincides in the strictl...