The goal of this note is to present some arguments leading the conjecture that a formally self-adjoint differential operator on closed manifold essentially if and only Hamiltonian flow its symbol complete. This holds for operators degree two circle, one any generic Lorentzian Laplacians surfaces.

We show how the twisting of spectral triples induces a transition from Euclidean to Lorentzian noncommutative geometry at level fermionic action. More specifically, we compute action for closed manifold, then that two-sheet and finally triple electrodynamics in signature. obtain Weyl Dirac equations signature (and temporal gauge). The twisted is shown be invariant under an Lorentz group. This p...

Fruitful ideas on how to quantize gravity are few and far between. In this paper, we give a complete description of a recently introduced non-perturbative gravitational path integral whose continuum limit has already been investigated extensively in d < 4, with promising results. It is based on a simplicial regularization of Lorentzian space-times and, most importantly, possesses a well-defined...

We prove the Morse relations for all geodesics connecting two non-conjugate points on a class of globally hyperbolic Lorentzian manifolds. We overcome the difficulties coming from the fact that the Morse index of every geodesic is infinite, and from the lack of the Palais-Smale condition, by using the Morse complex approach. Introduction Let M be a smooth connected manifold without boundary of ...

In this brief survey, we will remark the interaction among the Hessian tensor on a semi-Riemannian manifold and some of the several questions in Lorentzian (and also in semi-Riemannian) geometry where this 2−covariant tensor is involved. In particular, we deal with the characterization of Killing vector fields and the study of a set of consequences of energy conditions in the framework of stand...

Ricci solitons (RS) have an extensive background in modern physics and are extensively used cosmology general relativity. The focus of this work is to investigate almost (RAS) on Lorentzian manifolds with a special metric connection called semi-symmetric u-connection (SSM-connection). First, we show that any quasi-Einstein manifold having SSM-connection, whose RS, Einstein manifold. A similar c...