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.

As the foundation for a new computational implementation, we survey the calculation of the complex electrical conductivity tensor based on the KuboGreenwood (KG) formalism (J. Phys. Soc. Jpn. 12, 570 (1957); Proc. Phys. Soc. 71, 585 (1958)), with emphasis on derivations and technical aspects pertinent to use of projector augmented wave datasets with plane wave basis sets (Phys. Rev. B 50, 17953...

In the compact setting, Aazami and Ream (Lett Math Phys 112(4):17, 2002) proved that Riemannian metrics dual to a class of Lorentzian metrics, called (compact) general plane-fronted waves, are almost-Kähler. this note, we explain how construct extremal second-Chern–Einstein non-Kähler almost-Kähler those waves.

The standard text-book Jacobi equation (equation of geodesic deviation) arises by linearizing the geodesic equation around some chosen geodesic, where the linearization is done with respect to the coordinates and the velocities. The generalized Jacobi equation, introduced by Hodgkinson in 1972 and further developed by Mashhoon and others, arises if the linearization is done only with respect to...

Nanolithography using Non-Contact Mode Atomic Force Microscopy (NCM-AFM) is a promising method for the manufacture of nanometer sized devices. Compact models which suggest nanopatterned oxide dots with Gaussian or Lorentzian profiles are implemented in a Monte Carlo simulator in a level set environment. An alternative to compact models is explored with a physics based Monte Carlo model, where t...

We study a second example of the phenomenon studied in the article “The complex Lorentzian Leech lattice and the bimonster”. We find 14 roots in the automorphism group of the the quaternionic Lorentzian Leech lattice L that form the Coxeter diagram given by the incidence graph of projective plane over F2. We prove that the reflections in these 14 roots generate the automorphism group of L. The ...

A Lorentzian manifold is defined here as a smooth pseudoRiemannian manifold with a metric tensor of signature (2n + 1, 1). A Robinson manifold is a Lorentzian manifold M of dimension > 4 with a subbundle N of the complexification of TM such that the fibers of N → M are maximal totally null (isotropic) and [SecN,SecN ] ⊂ SecN . Robinson manifolds are close analogs of the proper Riemannian, Hermi...

We study a second example of the phenomenon studied in the article “The complex Lorentzian Leech lattice and the bimonster”. We find 14 reflections in the automorphism group of the the quaternionic Lorentzian Leech lattice L that form the Coxeter diagram given by the incidence graph of projective plane over F2. We prove that these 14 reflections generate the automorphism group of L. The investi...

LARS ANDERSSON, MATTIAS DAHL, AND RALPH HOWARD Abstract. Let g be a Lorentzian metric on the plane R2 that agrees with the standard metric g0 = −dx + dy outside a compact set and so that there are no conjugate points along any time-like geodesic of (R2 , g). Then (R2 , g) and (R2 , g0) are isometric. Further, if (M, g) and (M∗, g∗) are two dimensional compact time oriented Lorentzian manifolds ...