Essays about: "isometry"

Showing result 1 - 5 of 6 essays containing the word isometry.

1. 1. Octonion Algebras over Schemes and the Equivalence of Isotopes and Isometric Quadratic Forms

   University essay from Uppsala universitet/Matematiska institutionen

   Author : Victor Hildebrandsson; [2023]
   Keywords : Algebraic geometry; octonion algebras;

   Abstract : Octonion algebras are certain algebras with a multiplicative quadratic form. In 2019, Alsaody and Gille showed that, for octonion algebras over unital commutative rings, there is an equivalence between isotopes and isometric quadratic forms. READ MORE

3. 2. The Banach-Tarski paradox

   University essay from Göteborgs universitet/Institutionen för matematiska vetenskaper

   Author : Carl Elofsson; Adrian Nilsson; Nicolas Söderberg; Tim Westlund; [2022-07-04]
   Keywords : ;

   Abstract : In this thesis we present a proof of the Banach-Tarski paradox, a counterintuitive result that states that any ball in R3 can be cut into finitely many pieces and then be reassembled into two copies of the original ball. Since the result follows from the axiom of choice it is important for assessing its role as an axiom of mathematics. READ MORE

4. 3. Gravitation in Lorentz and Euclidean Geometry

   University essay from KTH/Fysik

   Author : Niki Wilhelmson; Johan Stoyanov; [2022]
   Keywords : gravitation; gravity; euclidean geometry; isometry; laplace; helmholtz; lorentz geometry; differential geometry; general relativity; special relativity; Einstein s field equations; Lovelock; Newton;

   Abstract : The aim of this work is to derive mathematical descriptions of gravitation. Postulating gravitation as a force field, Newton's law of gravitation is heuristically derived by considering linear differential operators invariant under euclidean isometries and by finding the fundamental solution to Helmholtz equation in three dimensions. READ MORE

5. 4. The GHP formalism, with applications to Petrov type III spacetimes

   University essay from Umeå universitet/Institutionen för fysik

   Author : Ekman Robin; [2014]
   Keywords : general relativity; spinors;

   Abstract : We give a review of the construction and application of spinor fields in general relativity and an account of the spinor-based Geroch-Held-Penrose (GHP) formalism. Specifically, we discuss using the GHP formalism to integrate Einstein's equations as suggested by Held  and developed by Edgar and Ludwig and discuss the similaritites with the Cartan-Karlhede classification of spacetimes. READ MORE

6. 5. The Square-Root Isometry of Coupled Quadratic Spaces : On the relation between vielbein and metric formulations of spin-2 interactions

   University essay from Stockholms universitet/Fysikum; Stockholms universitet/Oskar Klein-centrum för kosmopartikelfysik (OKC)

   Author : Kocic Mikica B.; [2014]
   Keywords : modified gravity; bigravity; bimetric theory; square-root isometry;

   Abstract : Bimetric theory is an extension to general relativity that introduces a secondary symmetric rank-two tensor field. This secondary spin-2 field is also dynamical, and to avoid the Boulware-Deser ghost issue, the interaction between the two fields is obtained through a potential that involes the matrix square-root of the tensors. READ MORE