The Riemann Legacy: Riemannian Ideas in Mathematics and Physics
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
1997
|
| Series: | Mathematics and Its Applications
417 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | very small domain (environment) affects through analytic continuation the whole of Riemann surface, or analytic manifold . Riemann was a master at applying this principle and also the first who noticed and emphasized that a meromorphic function is determined by its 'singularities'. Therefore he is rightly regarded as the father of the huge 'theory of singularities' which is developing so quickly and whose importance (also for physics) can hardly be overe~timated. Amazing and mysterious for our cognition is the role of Euclidean space. Even today many philosophers believe (following Kant) that 'real space' is Euclidean and other spaces being 'abstract constructs of mathematicians, should not be called spaces'. The thesis is no longer tenable - the whole of physics testifies to that. Nevertheless, there is a grain of truth in the 3 'prejudice': E (three-dimensional Euclidean space) is special in a particular way pleasantly familiar to us - in it we (also we mathematicians!) feel particularly 'confident' and move with a sense of greater 'safety' than in non-Euclidean spaces. For this reason perhaps, Riemann space M stands out among the multitude of 'interesting geometries'. For it is: 1. Locally Euclidean, i. e. , M is a differentiable manifold whose tangent spaces TxM are equipped with Euclidean metric Uxi 2. Every submanifold M of Euclidean space E is equipped with Riemann natural metric (inherited from the metric of E) and it is well known how often such submanifolds are used in mechanics (e. g. , the spherical pendulum) |
| Physical Description: | 1 Online-Ressource (XXII, 719 p) |
| ISBN: | 9789401589390 9789048148769 |
| DOI: | 10.1007/978-94-015-8939-0 |
Staff View
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| 500 | |a very small domain (environment) affects through analytic continuation the whole of Riemann surface, or analytic manifold . Riemann was a master at applying this principle and also the first who noticed and emphasized that a meromorphic function is determined by its 'singularities'. Therefore he is rightly regarded as the father of the huge 'theory of singularities' which is developing so quickly and whose importance (also for physics) can hardly be overe~timated. Amazing and mysterious for our cognition is the role of Euclidean space. Even today many philosophers believe (following Kant) that 'real space' is Euclidean and other spaces being 'abstract constructs of mathematicians, should not be called spaces'. The thesis is no longer tenable - the whole of physics testifies to that. Nevertheless, there is a grain of truth in the 3 'prejudice': E (three-dimensional Euclidean space) is special in a particular way pleasantly familiar to us - in it we (also we mathematicians!) feel particularly 'confident' and move with a sense of greater 'safety' than in non-Euclidean spaces. For this reason perhaps, Riemann space M stands out among the multitude of 'interesting geometries'. For it is: 1. Locally Euclidean, i. e. , M is a differentiable manifold whose tangent spaces TxM are equipped with Euclidean metric Uxi 2. Every submanifold M of Euclidean space E is equipped with Riemann natural metric (inherited from the metric of E) and it is well known how often such submanifolds are used in mechanics (e. g. , the spherical pendulum) | ||
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| illustrated | Not Illustrated |
| indexdate | 2024-10-22T12:01:09Z |
| institution | BVB |
| isbn | 9789401589390 9789048148769 |
| language | English |
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| spelling | Maurin, Krzysztof Verfasser aut The Riemann Legacy Riemannian Ideas in Mathematics and Physics by Krzysztof Maurin Dordrecht Springer Netherlands 1997 1 Online-Ressource (XXII, 719 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 417 very small domain (environment) affects through analytic continuation the whole of Riemann surface, or analytic manifold . Riemann was a master at applying this principle and also the first who noticed and emphasized that a meromorphic function is determined by its 'singularities'. Therefore he is rightly regarded as the father of the huge 'theory of singularities' which is developing so quickly and whose importance (also for physics) can hardly be overe~timated. Amazing and mysterious for our cognition is the role of Euclidean space. Even today many philosophers believe (following Kant) that 'real space' is Euclidean and other spaces being 'abstract constructs of mathematicians, should not be called spaces'. The thesis is no longer tenable - the whole of physics testifies to that. Nevertheless, there is a grain of truth in the 3 'prejudice': E (three-dimensional Euclidean space) is special in a particular way pleasantly familiar to us - in it we (also we mathematicians!) feel particularly 'confident' and move with a sense of greater 'safety' than in non-Euclidean spaces. For this reason perhaps, Riemann space M stands out among the multitude of 'interesting geometries'. For it is: 1. Locally Euclidean, i. e. , M is a differentiable manifold whose tangent spaces TxM are equipped with Euclidean metric Uxi 2. Every submanifold M of Euclidean space E is equipped with Riemann natural metric (inherited from the metric of E) and it is well known how often such submanifolds are used in mechanics (e. g. , the spherical pendulum) Riemann, Bernhard 1826-1866 (DE-588)118600869 gnd rswk-swf Mathematics Algebra Global analysis (Mathematics) Geometry Applications of Mathematics Analysis Mathematik Riemann, Bernhard 1826-1866 (DE-588)118600869 p 1\p DE-604 https://doi.org/10.1007/978-94-015-8939-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Maurin, Krzysztof The Riemann Legacy Riemannian Ideas in Mathematics and Physics Riemann, Bernhard 1826-1866 (DE-588)118600869 gnd Mathematics Algebra Global analysis (Mathematics) Geometry Applications of Mathematics Analysis Mathematik |
| subject_GND | (DE-588)118600869 |
| title | The Riemann Legacy Riemannian Ideas in Mathematics and Physics |
| title_auth | The Riemann Legacy Riemannian Ideas in Mathematics and Physics |
| title_exact_search | The Riemann Legacy Riemannian Ideas in Mathematics and Physics |
| title_full | The Riemann Legacy Riemannian Ideas in Mathematics and Physics by Krzysztof Maurin |
| title_fullStr | The Riemann Legacy Riemannian Ideas in Mathematics and Physics by Krzysztof Maurin |
| title_full_unstemmed | The Riemann Legacy Riemannian Ideas in Mathematics and Physics by Krzysztof Maurin |
| title_short | The Riemann Legacy |
| title_sort | the riemann legacy riemannian ideas in mathematics and physics |
| title_sub | Riemannian Ideas in Mathematics and Physics |
| topic | Riemann, Bernhard 1826-1866 (DE-588)118600869 gnd Mathematics Algebra Global analysis (Mathematics) Geometry Applications of Mathematics Analysis Mathematik |
| topic_facet | Riemann, Bernhard 1826-1866 Mathematics Algebra Global analysis (Mathematics) Geometry Applications of Mathematics Analysis Mathematik |
| url | https://doi.org/10.1007/978-94-015-8939-0 |
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