We introduce and study the notion of Sasaki–Weyl manifold, which is a natural generalization of the notion of Sasaki manifold. We construct a reduction of Sasaki–Weyl manifolds and we show that it commutes with several reductions already existing in the literature.

We give an elementary proof of the fact that any 4-dimensional para-Hermitian manifold admits a unique para-Kähler–Weyl structure. We then use analytic continuation to pass from the para-complex to the complex setting and thereby show that any 4-dimensional pseudo-Hermitian manifold also admits a unique Kähler–Weyl structure.

The aim of this paper is to extend the notion all known quasi-Einstein manifolds like generalized quasi-Einstein, mixed manifold, pseudo manifold and many more name it comprehensive quasi Einstein C(QE)$_{n}$. We investigate some geometric physical properties C(QE)$_{n}$ under certain conditions. study conformal conharmonic mappings between manifolds. Then we examine with harmonic Weyl tensor. ...

This note investigates the possibility of converses of the Weyl theorems that two conformally related metrics on a manifold have the same Weyl conformal tensor and that two projectively related connections on a manifold have the same Weyl projective tensor. It shows that, in all relevant cases, counterexamples to each of Weyl’s theorems exist except for his conformal theorem in the 4-dimensiona...

The relationship is established between the Fedosov deformation quantization of a general symplectic manifold and the BFV-BRST quantization of constrained dynamical systems. The original symplectic manifold M is presented as a second class constrained surface in the fibre bundle T * ρ M which is a certain modification of a usual cotangent bundle equipped with a natural symplectic structure. The...

There are also four appendices. Let K be a field of characteristic 0, and let C be a commutative K-algebra. which makes C into a Lie algebra, and is a biderivation (i.e. a derivation in each argument). The pair C, {−, −} is called a Poisson algebra. Poisson brackets arise in several ways. Example 1.1. Classical Hamiltonian mechanics. Here K = R, X is an even dimensional differentiable manifold ...

A tensor invariant is defined on a quaternionic contact manifold in terms of the curvature and torsion of the Biquard connection involving derivatives up to third order of the contact form. This tensor, called quaternionic contact conformal curvature, is similar to the Weyl conformal curvature in Riemannian geometry and to the Chern-Moser tensor in CR geometry. It is shown that a quaternionic c...

We study intersection numbers of invariant divisors in the toric manifold associated with the fan determined by the collection of Weyl chambers for each root system of classical type and of exceptional type G2. We give a combinatorial formula for intersection numbers of certain subvarieties which are naturally indexed by elements of the Weyl group. These numbers describe the ring structure of t...

On a (pseudo-) Riemannian manifold of dimension n > 3, the space of tensors which transform covariantly under Weyl rescalings of the metric is built. This construction is related to a Weyl-covariant operator D whose commutator [D,D] gives the conformally invariant Weyl tensor plus the Cotton tensor. So-called generalized connections and their transformation laws under diffeomorphisms and Weyl r...

A Bochner flat Kähler manifold is a Kähler manifold with vanishing Bochner curvature tensor. We shall give a uniformization of Bochner flat Kähler manifolds. One of the aims of this paper is to give a correction to the proof of our previous paper [9] concerning uniformization of Bochner flat Kähler manifolds. A Bochner flat locally conformal Kähler manifold is a locally conformal Kähler manifol...