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Absolute profinite rigidity and hyperbolic geometry [PDF]
Annals of Mathematics, 2020 We construct arithmetic Kleinian groups that are profinitely rigid in the absolute sense: each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients.
Bridson, M. R. +3 more
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Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry [PDF]
Advances in Mathematical Physics, 2016 The importance of Einstein’s geometrization philosophy, as an alternative to the least action principle, in constructing general relativity (GR), is illuminated. The role of differential identities in this philosophy is clarified.
M. I. Wanas +3 more
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Geometry without topology as a new conception of geometry [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 A geometric conception is a method of a geometry construction. The Riemannian geometric conception and a new T-geometric one are considered. T-geometry is built only on the basis of information included in the metric (distance between two points).
Yuri A. Rylov
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Axioms for Absolute Geometry. III [PDF]
Canadian Journal of Mathematics, 1969 This paper is a continuation of [1; 2]. In [2], I stated that I had been unable to construct examples of planes satisfying various conditions. Some of the examples that I have since constructed are given below. A discussion of one-dimensional absolute geometries, with examples, will be given in a separate paper. The relevant parts of [1] and [2] are [1,
J. F. Rigby
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Galois Sections in Absolute Anabelian Geometry [PDF]
Nagoya Mathematical Journal, 2005 AbstractWe show that isomorphisms between arithmetic fundamental groups of hyperbolic curves over p-adic local fields preserve the decomposition groups of all closed points (respectively, closed points arising from torsion points of the underlying elliptic curve), whenever the hyperbolic curves in question are isogenous to hyperbolic curves of genus ...
Shinichi Mochizuki
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A Global Approach to Absolute Parallelism Geometry [PDF]
Reports on Mathematical Physics, 2013 In this paper we provide a \emph{global} investigation of the geometry of parallelizable manifolds (or absolute parallelism geometry) frequently used for application. We discuss the different linear connections and curvature tensors from a global point of view.
Youssef, Nabil L., Elsayed, Waleed A.
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New Path Equations in Absolute Parallelism Geometry [PDF]
Astrophysics and Space Science, 2002 The Bazanski approach, for deriving the geodesic equations in Riemannian geometry, is generalized in the absolute parallelism geometry. As a consequence of this generalization three path equations are obtained. A striking feature in the derived equations
A. Einstein +10 more
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Bireflectionality in Absolute Geometry [PDF]
Canadian Mathematical Bulletin, 1989 AbstractIf G is any group then g ∊ G is called an involution if g ≠ 1 and g o g = 1. A group G is called bireflectional if every element in G is a product of two involutions. It is known that 2- dimensional, 3- dimensional, and some types of n-dimensional (n > 3) absolute geometries (in the sense of H. Kinder) are bireflectional. In this article the
Dragoslav Ljubić
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On absolute algebraic geometry the affine case [PDF]
Advances in Mathematics, 2021 34 pages, 2 ...
Connes, Alain, Consani, Caterina
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Parametric down-conversion from a wave-equations approach: geometry and absolute brightness [PDF]
, 2009 Using the approach of coupled wave equations, we consider spontaneous parametric down-conversion (SPDC) in the narrow-band regime and its relationship to classical nonlinear processes such as sum-frequency generation.
D. N. Klyshko +6 more
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