On the existence of a new class of semi-Riemannian manifolds

Abstract

In this paper, we will present some fixed point results for two classes of generalized contractions of Boyd-Wong type in partial b-metric spaces. More precisely, the structure of the paper is the following. In section one, we present some useful notions and results. The aim of section two is to introduce the concepts of Boyd-Wong F-contractions of type A and of type B and establish some new common fixed point results in partial b-metric spaces. We show the validity and superiority of our main results by suitable examples which are visualized by corresponding surfaces and related graphs. In section three, we correct some slip-ups in some recent papers. Finally, in section four, two applications to integral equation and periodic boundary value problem are included which make effective the new concepts and results.

Curvature properties of a special type of pure radiation metrics

“…holds on {x ∈ M : R = 0 and any one of S ∧ S, g ∧ S is non-zero at x} for some 1-forms Π, Ω, Θ and ω, called the associated 1-forms. Especially, if Ω = Θ = ω = 0 (resp., Θ = ω = 0 and Ω = ω = 0), then the manifold is called recurrent ( [30], [31], [32], [58]) (resp., weakly generalized recurrent ( [33], [47]) and hyper generalized recurrent ( [46], [48])) manifold.…”

“…(w 144 + w 133 ) − 2p 2 r (w33 + w 44 )) (w 33 + w 44 ) x 2 − Π 1 − Ω 1 , 0, (w 333 + w 344 ) x − 3w 33 − 3w 44 (w 33 + w 44 ) x , w 334 + w 444 w 33 + w 44 ,where Π 1 and Ω 1 are arbitrary scalars.Now from the values of the non-zero components of ∇T , we getT 11,1 + T 11,1 + T 11,1 = 3c 4 p 2 (−x 2 w 144 −x 2 w 133 +2p 2 rw 33 +2p 2 rw 44) − T 11,3 = c 4 p 2 (w 333 +w 344 )x…”

Curvature properties of Melvin magnetic metric

“…By curvature restricted geometric structures of a manifold mean the structures arose due to restriction of covariant derivative(s) on various curvature tensors of that manifold. Again, the study of local symmetry has been extended to various concepts such as recurrency [39,40,41], generalized recurrency [43,49,60,61,62,63,64], curvature 2-forms of recurrency [3,30], weakly symmetry [72], Chaki pseudosymmetry [6] etc. our aim in this paper is to investigate such type of geometry by means of restriction on several curvature tensors of Melvin magnetic metric (1.1).…”

Curvature properties of some 4-dimensional semi-Riemannian metrics

“…We note that every manifold of constant curvature and hence an Einstein manifold is of class A as well as B. The existence of both the classes is given in [82]. In a semi-Riemannian manifold (M, g), n ≥ 3, the Ricci tensor S is said to be a Codazzi tensor [48,106] (resp.…”

“…Again to generalize the notion of recurrent manifold in [96,98,[100][101][102][103] (see also [80]) the following four curvature conditions were introduced…”