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...

In this paper, we have proved that a projectively flat Sasakian manifold is an Einstein manifold. Also, if an Einstein-Sasakian manifold is projectively flat, then it is locally isometric with a unit sphere S(1). It has also been proved that if in an Einsten-Sasakian manifold the relation K(X, Y ).P = 0 holds, then it is locally isometric with a unit sphere S(1). AMS Mathematics Subject Classif...

Graphene as a two-dimensional topological semimetal has attracted much attention for its outstanding properties. In contrast, three-dimensional (3D) topological semimetals of carbon are still rare. Searching for such materials with salient physics has become a new direction in carbon research. Here, using first-principles calculations and tight-binding modeling, we propose a new class of Weyl s...

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 curvature is the one with a conformally flat but not necessarily flat metric ; we exhibit its 3-parameter distance and Weyl one-form. This extends previous analysis of Pedersen e...

We calculate the Weyl anomaly for conformal field theories that can be described via the adS/CFT correspondence. This entails regularizing the gravitational part of the corresponding supergravity action in a manner consistent with general covariance. Up to a constant, the anomaly only depends on the dimension d of the manifold on which the conformal field theory is defined. We present concrete ...

Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...

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...