In this paper, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined fo...

Let Mn be a Riemannian n-manifold. Denote by S(p) and Ric(p) the Ricci tensor and the maximum Ricci curvature on Mn, respectively. In this paper we prove that every C-totally real submanifolds of a Sasakian space form M̄2m+1(c) satisfies S ≤ ( (n−1)(c+3) 4 + n 2 4 H2)g, where H2 and g are the square mean curvature function and metric tensor on Mn, respectively. The equality holds identically if ...

Abstract Based on the geometry of codimension-2 surface in general spherically symmetric spacetime, we give a quasi-local definition photon sphere as well surface. This new is generalization one provided by Claudel, Virbhadra, and Ellis but without referencing any umbilical hypersurface spacetime. The effectively excludes spacetime gravity. application to Lemaître–Tolman–Bondi (LTB) model gravi...

∇XV = λX for every vector field X. (1.2) Here ∇ denotes the Levi-Civita connection of g. We call vector fields satisfying (1.2) closed conformal vector fields. They appear in the work of Fialkow [3] about conformal geodesics, in the works of Yano [7–11] about concircular geometry in Riemannian manifolds, and in the works of Tashiro [6], Kerbrat [4], Kühnel and Rademacher [5], and many other aut...

We investigate Kaluza-Klein metrics with a recurrent lightlike vector field over a pseudo-Riemannian manifold (B, g).

We give a unified derivation of the propagator in the gauges n.A = 0 for n timelike, spacelike or lightlike. We discuss the physical states and other physical questions.

We prove that the Lorentzian helicoid and Enneper’s surface are the unique properly embedded maximal surfaces bounded by a lightlike regular arc of mirror symmetry.

We show that the entropy created by Ohmic dissipation inside an accreting charged black hole may exceed the Bekenstein-Hawking entropy by a large factor. The second law of thermodynamics does not hold on spacelike slices inside these model black holes, even when the slices avoid Planck scale densities and curvatures. This result is distinct from, but consistent with, the fact that there is no e...

We show that the index of a lightlike geodesic in a conformally standard stationary spacetime (M0 × R, g) is equal to the index of its spatial projection as a geodesic of a Finsler metric F on M0 associated to (M0×R, g). Moreover we obtain the Morse relations of lightlike geodesics connecting a point p to a curve γ(s) = (q0, s) by using Morse theory on the Finsler manifold (M0, F ). To this end...