The Differential Geometry of Finsler Spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1959
|
| Schriftenreihe: | Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete
101 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The present monograph is motivated by two distinct aims. Firstly, an endeavour has been made to furnish a reasonably comprehensive account of the theory of Finsler spaces based on the methods of classical differential geometry. Secondly, it is hoped that this monograph may serve also as an introduction to a branch of differential geometry which is closely related to various topics in theoretical physics, notably analytical dynamics and geometrical optics. With this second object in mind, an attempt has been made to describe the basic aspects of the theory in some detail - even at the expense of conciseness - while in the more specialised sections of the later chapters, which might be of interest chiefly to the specialist, a more succinct style has been adopted. The fact that there exist several fundamentally different points of view with regard to Finsler geometry has rendered the task of writing a coherent account a rather difficult one. This remark is relevant not only to the development of the subject on the basis of the tensor calculus, but is applicable in an even wider sense. The extensive work of H. BUSEMANN has opened up new avenues of approach to Finsler geometry which are independent of the methods of classical tensor analysis. In the latter sense, therefore, a full description of this approach does not fall within the scope of this treatise, although its fundamental l significance cannot be doubted |
| Beschreibung: | 1 Online-Ressource (XVI, 284 p.) 1 illus |
| ISBN: | 9783642516108 9783642516122 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-642-51610-8 |
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| 500 | |a The present monograph is motivated by two distinct aims. Firstly, an endeavour has been made to furnish a reasonably comprehensive account of the theory of Finsler spaces based on the methods of classical differential geometry. Secondly, it is hoped that this monograph may serve also as an introduction to a branch of differential geometry which is closely related to various topics in theoretical physics, notably analytical dynamics and geometrical optics. With this second object in mind, an attempt has been made to describe the basic aspects of the theory in some detail - even at the expense of conciseness - while in the more specialised sections of the later chapters, which might be of interest chiefly to the specialist, a more succinct style has been adopted. The fact that there exist several fundamentally different points of view with regard to Finsler geometry has rendered the task of writing a coherent account a rather difficult one. This remark is relevant not only to the development of the subject on the basis of the tensor calculus, but is applicable in an even wider sense. The extensive work of H. BUSEMANN has opened up new avenues of approach to Finsler geometry which are independent of the methods of classical tensor analysis. In the latter sense, therefore, a full description of this approach does not fall within the scope of this treatise, although its fundamental l significance cannot be doubted | ||
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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-51610-8 |
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| institution | BVB |
| isbn | 9783642516108 9783642516122 |
| issn | 0072-7830 |
| language | English |
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| series2 | Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete |
| spelling | Rund, Hanno Verfasser aut The Differential Geometry of Finsler Spaces by Hanno Rund Berlin, Heidelberg Springer Berlin Heidelberg 1959 1 Online-Ressource (XVI, 284 p.) 1 illus txt rdacontent c rdamedia cr rdacarrier Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete 101 0072-7830 The present monograph is motivated by two distinct aims. Firstly, an endeavour has been made to furnish a reasonably comprehensive account of the theory of Finsler spaces based on the methods of classical differential geometry. Secondly, it is hoped that this monograph may serve also as an introduction to a branch of differential geometry which is closely related to various topics in theoretical physics, notably analytical dynamics and geometrical optics. With this second object in mind, an attempt has been made to describe the basic aspects of the theory in some detail - even at the expense of conciseness - while in the more specialised sections of the later chapters, which might be of interest chiefly to the specialist, a more succinct style has been adopted. The fact that there exist several fundamentally different points of view with regard to Finsler geometry has rendered the task of writing a coherent account a rather difficult one. This remark is relevant not only to the development of the subject on the basis of the tensor calculus, but is applicable in an even wider sense. The extensive work of H. BUSEMANN has opened up new avenues of approach to Finsler geometry which are independent of the methods of classical tensor analysis. In the latter sense, therefore, a full description of this approach does not fall within the scope of this treatise, although its fundamental l significance cannot be doubted Mathematics Mathematics, general Mathematik Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Finsler-Raum (DE-588)4154449-3 gnd rswk-swf Finsler-Geometrie (DE-588)4451048-2 gnd rswk-swf Finsler-Raum (DE-588)4154449-3 s Differentialgeometrie (DE-588)4012248-7 s 1\p DE-604 Finsler-Geometrie (DE-588)4451048-2 s 2\p DE-604 https://doi.org/10.1007/978-3-642-51610-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rund, Hanno The Differential Geometry of Finsler Spaces Mathematics Mathematics, general Mathematik Differentialgeometrie (DE-588)4012248-7 gnd Finsler-Raum (DE-588)4154449-3 gnd Finsler-Geometrie (DE-588)4451048-2 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4154449-3 (DE-588)4451048-2 |
| title | The Differential Geometry of Finsler Spaces |
| title_auth | The Differential Geometry of Finsler Spaces |
| title_exact_search | The Differential Geometry of Finsler Spaces |
| title_full | The Differential Geometry of Finsler Spaces by Hanno Rund |
| title_fullStr | The Differential Geometry of Finsler Spaces by Hanno Rund |
| title_full_unstemmed | The Differential Geometry of Finsler Spaces by Hanno Rund |
| title_short | The Differential Geometry of Finsler Spaces |
| title_sort | the differential geometry of finsler spaces |
| topic | Mathematics Mathematics, general Mathematik Differentialgeometrie (DE-588)4012248-7 gnd Finsler-Raum (DE-588)4154449-3 gnd Finsler-Geometrie (DE-588)4451048-2 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Differentialgeometrie Finsler-Raum Finsler-Geometrie |
| url | https://doi.org/10.1007/978-3-642-51610-8 |
| work_keys_str_mv | AT rundhanno thedifferentialgeometryoffinslerspaces |