By using variational methods, we study the existence and multiplicity of trajec-tories under a vectorial potential on (standard) stationary Lorentzian manifolds possibly with boundary. 1. Introduction and statement of the results. The pair (ᏸ,g) is called Lorentzian manifold if ᏸ is a connected finite-dimensional smooth manifold with dim ᏸ ≥ 2 and g is a Lorentzian metric on ᏸ, that is, g is a ...

In this paper, we introduce a concept of B-minimal sub-manifolds and discuss the stability of such a sub-manifold in a Riemannian manifold (M, g). Assume B(x) is a smooth function on M . By definition, we call a sub-manifold Σ B-minimal in (M, g) if the product sub-manifold Σ × S1 is a minimal sub-manifold in a warped product Riemannian manifold (M×S1, g+ e2B(x)dt2), so its stability is closely...

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...

Let Fm = (M,F ) be a Finsler manifold and G be the Sasaki– Finsler metric on the slit tangent bundle TM0 = TM {0} of M . We express the scalar curvature ρ̃ of the Riemannian manifold (TM0, G) in terms of some geometrical objects of the Finsler manifold Fm. Then, we find necessary and sufficient conditions for ρ̃ to be a positively homogenenous function of degree zero with respect to the fiber coo...

Whenever a finitely generated group $G$ acts properly discontinuously by isometries on metric space $X$, there is an induced uniform embedding (a Lipschitz and uniformly proper map) $\rho: G \rightarrow X$ given mapping to orbit. We study when difference between acting contractible $n$-manifold into $n$-manifold. For example, Kapovich Kleiner showed that are torsion-free hyperbolic groups embed...

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...

defined by (a, fl)o = (ctujl)[M] is a non-singular (l)k-symmetric bilinear pairing. The isometry class of the rational intersection form is determined by the rank if k is odd and by the rank and signature if k is even. We wish to make a corresponding analysis of the equivariant intersection form in the case where M is the total space of a finite G-cover. Let G be a finite group and w: G + { f l...