We study the quarter-symmetric metric A-connection on a cosymplectic manifold. Observing linearly independent curvature tensors with respect to A-connection, we construct Weyl projective tensor In this way, obtain new conditions for manifold be projectively flat. At end of paper, define η-Einstein manifolds θ-th kind and prove that they coincide

‎In this paper we first obtain the non-Riemannian Randers metrics of Douglas type on two-step homogeneous nilmanifolds of dimension five‎. ‎Then we explicitly give the flag curvature formulae and the $S$-curvature formulae for the Randers metrics of Douglas type on these spaces‎. ‎Moreover‎, ‎we prove that the only simply connected five-dimensional two-step homogeneous Randers nilmanifolds of D...

In this paper we study *-Conformal {\eta}-Ricci soliton on Sasakian manifolds. Here, discuss some curvature properties manifold admitting soliton. We obtain significant results in manifolds satisfying R({\xi},X).S = 0, S({\xi},X).R {\overline}P({\xi},X).S where {\overline}P is Pseudo-projective tensor.The conditions for {\Phi}-conharmonically flat and {\Phi}-projectively have been obtained arti...

This article is a survey of recent work [15, 6, 7, 13] developing a new approach to quantization based on the equivariance with respect to some Lie group of symmetries. Examples are provided by conformal and projective differential geometry: given a smooth manifold M endowed with a flat conformal/projective structure, we establish a canonical isomorphism between the space of symmetric contravar...

We show that coinvariants of modules over vertex operator algebras give rise to quasi-coherent sheaves on moduli stable pointed curves. These generalize Verlinde bundles or vector conformal blocks defined using affine Lie studied first by Tsuchiya-Kanie, Tsuchiya-Ueno-Yamada, and extend work a number researchers. The carry twisted logarithmic D-module structure, hence support projectively flat ...