We obtain some results in both, Lorentz and Finsler geometries, by using a correspondence between the conformal structure of standard stationary spacetimes on M = R × S and Randers metrics on S. In particular: (1) For stationary spacetimes: we give a simple characterization on when R×S is causally continuous or globally hyperbolic (including in the latter case, when S is a Cauchy hypersurface),...

I present an approach to gravity in which the spacetime metric is constructed from a non-Abelian gauge potential with values in the Lie algebra of the group U(2) (or the Lie algebra of quaternions). If the curvature of this potential vanishes, the metric reduces to a canonical curved background form reminiscent of the Friedmann S cosmological metric.

We assume that the manifold with boundary, X, has a SpinC-structure with spinor bundle S /. Along the boundary, this structure agrees with the structure defined by an infinite order integrable almost complex structure and the metric is Kähler. In this case the SpinC-Dirac operator ð agrees with ∂̄ + ∂̄∗ along the boundary. The induced CR-structure on bX is integrable and either strictly pseudocon...

The symmetric group S , is a metric space with distance d(a , b ) = IE(a-'b)( where E ( c ) is the set of points moved by c E S,. Let L be a given subset of {I. 2, . . . , n}, a permutation clique A = A(L, n ) is any subset A c S , with d(a, b ) E L whenever a, b E A , a # b. We give a framework of new and known information o n some special A = A ( L , n): maximal, largest, largest subgroups of...

Let S be the unit sphere in the Euclidean space R, and let e be the standard metric on S induced from R. Suppose that (u, ρ) are the spherical coordinates in R, where u ∈ S, ρ ∈ [0,∞). By choosing the smooth function φ(ρ) := sinh ρ on [0,∞) we can define a Riemannian metric h on the set {(u, ρ) : u ∈ S, 0 ≤ ρ < ∞} as follows h = dρ + φ(ρ)e. This gives the space form R(−1) which is the hyperboli...

Objectives: To establish a fixed-point theorem on complete S -metric space. Methods: By using (E.A)-property of self-maps and applying the concept strong comparison function. Findings: Obtained unique common for four S-metric space validated it with suitable example. Novelty: utilizing weak compatibility together (E.A)- property, fixed point is obtained which more robust generalization existing...

A resolving set for a graph Γ is a collection of vertices S, chosen so that for each vertex v, the list of distances from v to the members of S uniquely specifies v. The metric dimension μ(Γ) is the smallest size of a resolving set for Γ. We consider the metric dimension of the dual polar graphs, and show that it is at most the rank over R of the incidence matrix of the corresponding polar spac...

Suppose M is an n-dimensional Kähler manifold and L is an ample line bundle over M . Let the Kähler form of M be ωg and the Hermitian metric of L be H. We assume that ωg is the curvature of H, that is, ωg = Ric(H). The Kähler metric of ωg is called a polarized Kähler metric on M . Using H and ωg, for any positive integer m, H 0(M,Lm) becomes a Hermitian inner product space. We use the following...

in this paper the general relatively isotropic l -curvature finsler metrics are studied. it isshown that on constant relatively landsberg spaces, the concepts of weakly landsbergian, landsbergianand generalized landsbergian metrics are equivalent. some necessary conditions for a relativelyisotropic l -curvature finsler metric to be a riemannian metric are also found.

A metric of non-negative sectional curvature on the direct product S2 × S2 of two two-spheres may be introduced as follows: take spheres (S2 i , gi), i = 1, 2 with rotationally symmetric metrics of non-negative curvature and consider the factor space of (S2, g1) × (S2, g2) × S1 by the action of the family of isometries Ĩτ (φ1, φ2) acting as the composition of a rotation of the first factor by a...