| Description |
1 online resource (351 p.) |
| Contents |
Cover -- Half Title -- Title Page -- Copyright Page -- Contents -- Preface of the Portuguese Version -- Preface -- Chapter 1: Welcome to Lorentz-Minkowski Space -- 1.1. PSEUDO-EUCLIDEAN SPACES -- 1.1.1. Defining Rnn -- 1.1.2. The causal character of a vector in Rnn -- 1.2. SUBSPACES OF Rnn -- 1.3. CONTEXTUALIZATION IN SPECIAL RELATIVITY -- 1.4. ISOMETRIES IN Rnn -- 1.5. INVESTIGATING O1(2,R) AND O1(3,R) -- 1.5.1. The group O1(2,R) in detail -- 1.5.2. The group O1(3,R) in (a little less) detail -- 1.5.3. Rotations and boosts -- 1.6. CROSS PRODUCT IN Rnn -- 1.6.1. Completing the toolbox |
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Chapter 2: Local Theory of Curves -- 2.1. PARAMETRIZED CURVES IN Rnn -- 2.2. CURVES IN THE PLANE -- 2.3. CURVES IN SPACE -- 2.3.1. The Frenet-Serret trihedron -- 2.3.2. Geometric effects of curvature and torsion -- 2.3.3. Curves with degenerate osculating plane -- Chapter 3: Surfaces in Space -- 3.1. BASIC TOPOLOGY OF SURFACES -- 3.2. CAUSAL TYPE OF SURFACES, FIRST FUNDAMENTAL FORM -- 3.2.1. Isometries between surfaces -- 3.3. SECOND FUNDAMENTAL FORM AND CURVATURES -- 3.4. THE DIAGONALIZATION PROBLEM -- 3.4.1. Interpretations for curvatures -- 3.5. CURVES IN A SURFACE |
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3.6. GEODESICS, VARIATIONAL METHODS AND ENERGY -- 3.6.1. Darboux-Ribaucour frame -- 3.6.2. Christoffel symbols -- 3.6.3. Critical points of the energy functional -- 3.7 THE FUNDAMENTAL THEOREM OF SURFACES -- 3.7.1. The compatibility equations -- Chapter 4: Abstract Surfaces and Further Topics -- 4.1. PSEUDO-RIEMANNIAN METRICS -- 4.2. RIEMANN'S CLASSIFICATION THEOREM -- 4.3. SPLIT-COMPLEX NUMBERS AND CRITICAL SURFACES -- 4.3.1. A brief introduction to split-complex numbers -- 4.3.2. Bonnet rotations -- 4.3.3. Enneper-Weierstrass representation formulas |
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4.4. DIGRESSION: COMPLETENESS AND CAUSALITY -- Appendix: Some Results from Differential Calculus -- Bibliography -- Index |
| Notes |
Description based upon print version of record |
| Form |
Electronic book
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| Author |
Lymberopoulos, Alexandre
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| ISBN |
9781000223347 |
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1000223345 |
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