We give a causal version of Eisenhart's geodesic characterization of classical mechanics. We emphasize the geometric, coordinate independent properties needed to express Eisenhart's theorem in light of modern studies on the Bargmann structures (lightlike dimensional reduction). The construction of the space metric, Coriolis 1-form and scalar potential through which the theorem is formulated is ...

Abstract A well-known application of the Raychaudhuri equation shows that, under geodesic completeness, totally null hypersurfaces are unique which satisfy that Ricci curvature is nonnegative in direction. The proof this fact based on a direct analysis differential inequality. In paper, we show, without assuming an inequality involving squared mean and compact three-dimensional hypersurface als...

In this paper, we study pseudo-slant submanifolds of nearly Kaehler manifolds. A classification theorem on a totally umbilical pseudo-slant submanifold of a nearly Kaehler manifold is proved. 2000 Mathematics Subject Classification: 53C40, 53B25, 53C15.

It is shown that, on a manifold with a Finsler metric of Lorentzian signature, the lightlike geodesics satisfy the following variational principle. Among all lightlike curves from a point q (emission event) to a timelike curve γ (worldline of receiver), the lightlike geodesics make the arrival time stationary. Here “arrival time” refers to a parametrization of the timelike curve γ. This variati...

We introduce new concepts and properties of lightlike distributions and foliations (of dimension and co-dimension 1) in a space-time manifold of dimension n, from a purely geometric point of view. Given an observer and a lightlike distribution Ω of dimension or co-dimension 1, its lightlike direction is broken down into two vector fields: a timelike vector field U representing the observer and ...

Umbilical endometrioma is a rare condition, with an estimated incidence of 0.5%-1% in all patients with endometrial ectopia. Spontaneous abdominal wall endometriosis is an even rarer and more unusual condition with unclear pathogenetic mechanisms. A 44-year-old parous woman presented with an umbilical skin lesion, and no history of bleeding from the umbilical mass or swelling in the umbilical a...

We study field theories in the limit that a compactified dimension becomes lightlike. In almost all cases the amplitudes at each order of perturbation theory diverge in the limit, due to strong interactions among the longitudinal zero modes. The lightlike limit generally exists nonperturbatively, but is more complicated than might have been assumed. Some implications for the matrix theory conje...