Concepts and techniques from the theory of G-structures of higher order are applied to the study of certain structures (volume forms, conformal structures, linear connections and projective structures) defined on a pseudo-Riemannian manifold. Several relationships between the structures involved have been investigated. The operations allowed on G-structures, such as intersection, inclusion, red...

We provide necessary and sufficient conditions for some particular couples ( g , ? ) of pseudo-Riemannian metrics affine connections to be statistical structures if we have gradient almost Einstein, Ricci, Yamabe solitons, or a more general type solitons on the manifold. In cases, establish formula volume manifold give lower an upper bound norm Ricci curvature tensor field.

The present paper shows that general relativity in the Arnowitt-Deser-Misner formalism admits a BV-BFV formulation. More precisely, for any d + 1 � 2 (pseudo-) Riemannian manifold M with spacelike or time-like boundary components, the BV data on the bulk induces compatible BFV data on the boundary. As a byproduct, the usual canonical formulation of general relativity is recovered in a straightf...

Let (M, g) be a complete Riemannian manifold with no conjugate points and f : (M, g) → (B, gB) a principal G-bundle, where G is a Lie group acting by isometries and B the smooth quotient with gB the Riemannian submersion metric. We obtain a characterization of conjugate point-free quotients (B, gB) in terms of symplectic reduction and a canonical pseudo-Riemannian metric on the tangent bundle T...

in this paper, we discuss the geometric properties of solution and lower bound estimate of ∆um−1 of the cauchy problem for a degenerate parabolic equation with periodic source term ut =∆um+ upsint. our objective is to show that: (1)with continuous variation of time t, the surface ϕ = [u(x,t)]mδq is a complete riemannian manifold floating in space rn+1and is tangent to the space rn at ∂h0(t); (2...

We introduce the concept of quasi-semi-Weyl structure, we provide a couple ways for constructing quasi-statistical and structures by means pseudo-Riemannian metric, an affine connection tensor field on smooth manifold, place these in relation with one another.

This article aims to study almost α-Kenmotsu pseudo-Riemannian structure. We first focus on the concept of structure and its basic properties. Then, we shall prove some fundamental formulas classification results such manifolds with CR-integrable Finally, illustrative examples manifold are given.

We consider the unit tangent sphere bundle of Riemannian manifold ( M, g ) with g-natural metric G̃ and we equip it to an almost contact B-metric structure. Considering this structure, we show that there is a direct correlation between the Riemannian curvature tensor of ( M, g ) and local symmetry property of G̃. More precisely, we prove that the flatness of metric g is necessary and sufficien...

Conformally flat pseudo-Riemannian manifolds with generalized Ricci recurrent, $(GR)_n$ structure are completely classified in this short report. A conformally recurrent manifold is shown to be either a de Sitter space or an anti-de space. In particular, spacetime must spacetime.