According to the formula of translational motion of vector along an infinitesimal closed curve in gravitational space, this article shows that the space and time both are quantized; the called center singularity of Schwarzschild metric does not exist physically, and Einstein’s theory of gravity is compatible with the traditional quantum theory in essence; the quantized gravitational space is ju...

We wish to describe how the hyperbolic geometry of a Riemann surface of genus g y g > 2, leads to a symplectic geometry on Tg, the genus g Teichmüller space, and ~Mg, the moduli space of genus g stable curves. The symplectic structure has three elements: the Weil-Petersson Kahler form, the FenchelNielsen vector fields t+, and the geodesic length functions I*. Weil introduced a Kahler metric for...

We consider a generalization of Riemannian geometry that naturally arises in the framework of control theory. Let X and Y be two smooth vector fields on a two-dimensional manifold M . If X and Y are everywhere linearly independent, then they define a classical Riemannian metric on M (the metric for which they are orthonormal) and they give to M the structure of metric space. If X and Y become l...

We introduce the notion of λ-spaces which is much weaker than cone metric spaces defined by Huang and X. Zhang 2007 . We establish some critical point theorems in the setting of λ-spaces and, in particular, in the setting of complete cone metric spaces. Our results generalize the critical point theorem proposed by Dancs et al. 1983 and the results given by Khanh and Quy 2010 to λ-spaces and con...

We consider modified dispersion relations in quantum field theory on curved space-time. Such relations, despite breaking the local Lorentz invariance at high energy, are considered in several phenomenological approaches to quantum gravity. Their existence involves a modification of the formalism of quantum field theory, starting from the problem of finding the scalar Green’s functions up to the...

We show that the half-line m functions associated with vector-valued discrete Schrödinger operators are elements in Siegel upper half space. introduce a metric on space of to these operators. Then, we action transfer matrices is distance decreasing.

We prove a related fixed point theorem for n mappings which arenot necessarily continuous in n fuzzy metric spaces using an implicit relationone of them is a sequentially compact fuzzy metric space which generalizeresults of Aliouche, et al. [2], Rao et al. [14] and [15].

The paper presents an extension of the geometric quantization procedure to integrable, big-isotropic structures. We obtain a generalization of the cohomology integrality condition, we discuss geometric structures on the total space of the corresponding principal circle bundle and we extend the notion of a polarization. 1 Big-isotropic structures Weak-Hamiltonian functions belong to the framewor...

We study how convergence of an observer whose state lives in a copy of the given system’s space can be established using a Riemannian metric. We show that the existence of an observer guaranteeing the property that a Riemannian distance between system and observer solutions is nonincreasing implies that the Lie derivative of the Riemannian metric along the system vector field is conditionally n...

We consider a generalization of Riemannian geometry that naturally arises in the framework of control theory. Let X and Y be two smooth vector fields on a two-dimensional manifold M . If X and Y are everywhere linearly independent, then they define a classical Riemannian metric on M (the metric for which they are orthonormal) and they give to M the structure of metric space. If X and Y become l...