It is demonstrated that any two reference frames (RFs), which are uniformly and rectilinearly moving relative to each other, can be adjusted via (possibly anisotropic) rescaling and re-synchronization so that the resulting pair of RFs is Lorentzian; this statement remains true if the word “Lorentzian” is replaced by “Galilean” or “Riemannian”, i.e., if a finite positive value of c is replaced b...

Connes’ functional formula of the Riemannian distance is generalized to the Lorentzian case using the so-called Lorentzian distance, the d’Alembert operator and the causal functions of a globally hyperbolic spacetime. As a step of the presented machinery, a proof of the almosteverywhere smoothness of the Lorentzian distance considered as a function of one of the two arguments is given. Afterwar...

This research article attempts to investigate anti-invariant Lorentzian submersions and the Lagrangian (LLS) from concircular structure [in short (LCS) n ] manifolds onto semi-Riemannian with relevant non-trivial examples. It is shown that horizontal distributions of such are not integrable their fibers totally geodesic. As a result, they can be geodesic maps. Anti-invariant also explored for h...

Introduction: Recently reported contrast in MR gradient echo phase images between brain gray matter (GM) and white matter (WM) holds a great promise for in vivo study of biological tissue structure with substantially improved resolution, which is profoundly enhanced at high field [1]. Possible origins of this contrast have been debated but mostly attributed to magnetic susceptibility effects. I...

A maximal surface S with isolated singularities in a complete flat Lorentzian 3-manifold N is said to be entire if it lifts to a (periodic) entire multigraph S̃ in L. In addition, S is called of finite type if it has finite topology, finitely many singular points and S̃ is finitely sheeted. Complete and proper maximal immersions with isolated singularities in N are entire, and entire embedded max...