It is proved that any compact almost Kähler, Einstein 4-manifold whose fundamental form is a root of the Weyl tensor is necessarily Kähler.

Construction of an infinite dimensional differentiable manifold R∞ not modelled on any Banach space is proposed. Definition, metric and differential structures of a Weyl algebra (P ∗ p M [[~]], ◦) and a Weyl algebra bundle (P∗M[[~]], ◦) are presented. Continuity of the ◦-product in the Tichonov topology is proved. Construction of the ∗-product of the Fedosov type in terms of theory of connectio...

The G-function associated to the semisimple Frobenius manifold C/W (where W is a Coxeter group or an extended affine Weyl group) is studied. The general form of the Gfunction is given in terms of a logarithmic singularity over caustics in the manifold. The main result in this paper is a universal formula for the G-function corresponding to the Frobenius manifold C/W̃ (An−1) , where W̃ (An−1) is a...

The notion of the Wick star-product is covariantly introduced for a general symplectic manifold equipped with two transverse polarisations. Along the lines of Fedosov method, the explicit procedure is given to construct the Wick symbols on the manifold. The cohomological obstruction is identified to the equivalence between the Wick star-product and the Fedosov one. In particular in the Kähler c...

Let G be a 1-connected, almost-simple Lie group over a local field and S a subsemigroup of G with non-empty interior. The action of the regular hyperbolic elements in the interior of S on the flag manifold G/P and on the associated Euclidean building allows us to prove that the invariant control set exists and is unique. We also provide a characterization of the set of transitivity of the contr...

In the present work, generalized recurrent and concircularly Weyl manifolds are examined. We define nearly quasi-Einstein we proved that if a or manifold admits special concircular vector field, then reduces to manifold. Also, some other results presented.

A strict quantization of a Poisson manifold P on a subset I ⊆ R containing 0 as an accumulation point is defined as a continuous field of C∗-algebras {Ah̄}h̄∈I , with A0 = C0(P ), a dense subalgebra Ã0 of C0(P ) on which the Poisson bracket is defined, and a set of continuous cross-sections {Q(f )} f∈Ã0 for which Q0(f ) = f . Here Qh̄(f ∗) = Qh̄(f )∗ for all h̄ ∈ I , whereas for h̄ → 0 one requires t...

Weyl geometry is a natural extension of conformal with covariance mediated by connection. We generalize the Fefferman-Graham (FG) ambient construction for manifolds to corresponding manifolds. first introduce Weyl-ambient metric motivated Weyl-Fefferman-Graham (WFG) gauge. From top-down perspective, we show that space as pseudo-Riemannian induces codimension-2 geometry. Then, from bottom-up sta...

The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects—where the body is stress-free—is a flat Weyl manifold, i.e. a manifold with an affine connection that has non-metricity with vanishing traceless part, but...

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 : • ...