Abstract: Completing the results achieved in a previous paper, we prove the symmetry of Hadamard/Seeley-deWitt off-diagonal coefficients in smooth D-dimensional Lorentzian manifolds. To this end, it is shown that, in any Lorentzian manifold, a sort of “local Wick rotation” of the metric can be performed provided the metric is a locally analytic function of the coordinates and the coordinates ar...

‎In this work‎, ‎first the differential equation characterizing position vector‎ ‎of spacelike curve is obtained in Lorentzian plane $mathbb{L}^{2}.$ Then the‎ ‎special curves mentioned above are studied in Lorentzian plane $mathbb{L}%‎‎^{2}.$ Finally some characterizations of these special curves are given in‎ ‎$mathbb{L}^{2}.$‎

The object of this paper is to study $(epsilon)$-Lorentzian para-Sasakian manifolds. Some typical identities for the curvature tensor and the Ricci tensor of $(epsilon)$-Lorentzian para-Sasakian manifold are investigated. Further, we study globally $phi$-Ricci symmetric and weakly $phi$-Ricci symmetric $(epsilon)$-Lorentzian para-Sasakian manifolds and obtain interesting results.

In this paper, hyperbolic spinor representations of space curves are studied according to the q-frame in E_1^3. The formulations calculated for spacelike and timelike tangent vector cases Moreover, relationships equations between Frenet frame Lorentz expressed. results supported with some theorems.