In this paper, we extend Sasaki metric for tangent bundle of a Riemannian manifold and Sasaki-Mok metric for the frame bundle of a Riemannian manifold [I] to the case of a semi-Riemannian vector bundle over a semi- Riemannian manifold. In fact, if E is a semi-Riemannian vector bundle over a semi-Riemannian manifold M, then by using an arbitrary (linear) connection on E, we can make E, as a...

the objective of this work was to develop a new design of an intake manifold through a 1d simulation. it is quite familiar that a duly designed intake manifold is essential for the optimal performance of an internal combustion engine. air flow inside the intake manifold is one of the important factors, which governs the engine performance and emissions. hence the flow phenomenon inside the inta...

Communicated by Abraham A. Ungar Abstract. In this paper, we investigate the reflections in Minkowski three-space by three different approaches. Firstly, we define Lorentzian reflections with Lorentzian inner product. Then, we examine Lorentzian reflections in view of Lorentzian Householder matrices. Finally, we use pure split quaternions to derive Lorentzian reflections. For each case, we find...

In a general Lorentzian manifold M, the past lightcone of point is proper subset M that does not carry enough information to determine rest M. That said, if globally hyperbolic Cauchy development vacuum initial data on surface S and there whose contains S, then contents such determines all (up isometry). We show some results describe what properties guarantee lightcones do indeed or at least si...

Sufficient conditions for a Lorentzian generalized quasi-Einstein manifold M,g,f,μ to be Robertson–Walker spacetime with Einstein fibers are derived. The Ricci tensor in this case gains the perfect fluid form. Likewise, it is proven that λ,n+m-Einstein M,g,w having harmonic Weyl tensor, ∇jw∇mwCjklm=0 and ∇lw∇lw<0 reduces fibers. Finally, if φ=−m∇lnw φRic-vector field on M an ψ=∇w ψRic-vector...

In this review paper, we discuss the relation between recent advances in theory of partial differential equations and their applications to quantum field on curved spacetimes. particular, focus hyperbolic propagators role they play construction physically admissible states—the so-called Hadamard states—on globally We will notion a propagator how it can be constructed an explicit invariant fashi...

For a complete Riemannian manifold M with (1,1)-elliptic Codazzi self-adjoint tensor field A, we use the divergence type operator $${L_A}(u): = div(A\nabla u)$$ and an extension of Ricci to extend some major comparison theorems in geometry. In fact such as mean curvature theorem, Bishop–Gromov volume Cheeger–Gromoll splitting theorem their famous topological consequences. Also get upper bound f...

the present article serves the purpose of pursuing geometrization of heat flow on volumetrically isothermal manifold by means of rf approach. in this article, we have analyzed the evolution of heat equation in a 3-dimensional smooth isothermal manifold bearing characteristics of riemannian manifold and fundamental properties of thermodynamic systems. by making use of the notions of various curva...

We consider 1 spacelike Killing vector field reductions of 4-d vacuum general relativity. We restrict attention to cases in which the manifold of orbits of the Killing field is R. The reduced Einstein equations are equivalent to those for Lorentzian 3-d gravity coupled to an SO(2,1) nonlinear sigma model on this manifold. We examine the theory in terms of a Hamiltonian formulation obtained via ...