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Discontinuous groups of isometries in the hyperbolic plane [[electronic resource] /] / Werner Fenchel, Jakob Nielsen ; edited by Asmus L. Schmidt
| Discontinuous groups of isometries in the hyperbolic plane [[electronic resource] /] / Werner Fenchel, Jakob Nielsen ; edited by Asmus L. Schmidt |
| Autore | Fenchel W (Werner), <1905-> |
| Pubbl/distr/stampa | Berlin ; ; New York, : Walter de Gruyter, 2003 |
| Descrizione fisica | 1 online resource (388 p.) |
| Disciplina | 514/.2 |
| Altri autori (Persone) |
NielsenJakob <1890-1959.>
SchmidtAsmus L |
| Collana | De Gruyter studies in mathematics |
| Soggetto topico |
Discontinuous groups
Isometrics (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 3-11-089135-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Chapter I. Möbius transformations and non-euclidean geometry. -- §1 Pencils of circles - inversive geometry -- §2 Cross-ratio -- §3 Möbius transformations, direct and reversed -- §4 Invariant points and classification of Möbius transformations -- §5 Complex distance of two pairs of points -- §6 Non-euclidean metric -- §7 Isometric transformations -- §8 Non-euclidean trigonometry -- §9 Products and commutators of motions -- Chapter II. Discontinuous groups of motions and reversions. -- §10 The concept of discontinuity -- §11 Groups with invariant points or lines -- §12 A discontinuity theorem -- §13 ℱ-groups. Fundamental set and limit set -- §14 The convex domain of an ℱ-group. Characteristic and isometric neighbourhood -- §15 Quasi-compactness modulo ℱ and finite generation of ℱ -- Chapter III. Surfaces associated with discontinuous groups. -- §16 The surfaces D modulo ℭ and K(ℱ) modulo ℱ -- §17 Area and type numbers -- Chapter IV. Decompositions of groups. -- §18 Composition of groups -- §19 Decomposition of groups -- §20 Decompositions of ℱ-groups containing reflections -- §21 Elementary groups and elementary surfaces -- §22 Complete decomposition and normal form in the case of quasi-compactness -- §23 Exhaustion in the case of non-quasi-compactness -- Chapter V. Isomorphism and homeomorphism. -- §24 Topological and geometrical isomorphism -- §25 Topological and geometrical homeomorphism -- §26 Construction of g-mappings. Metric parameters. Congruent groups -- Symbols and definitions -- Alphabets -- Bibliography -- Index |
| Record Nr. | UNINA-9910462018803321 |
Fenchel W (Werner), <1905->
|
||
| Berlin ; ; New York, : Walter de Gruyter, 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Discontinuous groups of isometries in the hyperbolic plane [[electronic resource] /] / Werner Fenchel, Jakob Nielsen ; edited by Asmus L. Schmidt
| Discontinuous groups of isometries in the hyperbolic plane [[electronic resource] /] / Werner Fenchel, Jakob Nielsen ; edited by Asmus L. Schmidt |
| Autore | Fenchel W (Werner), <1905-> |
| Pubbl/distr/stampa | Berlin ; ; New York, : Walter de Gruyter, 2003 |
| Descrizione fisica | 1 online resource (388 p.) |
| Disciplina | 514/.2 |
| Altri autori (Persone) |
NielsenJakob <1890-1959.>
SchmidtAsmus L |
| Collana | De Gruyter studies in mathematics |
| Soggetto topico |
Discontinuous groups
Isometrics (Mathematics) |
| ISBN | 3-11-089135-2 |
| Classificazione | SK 380 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Chapter I. Möbius transformations and non-euclidean geometry. -- §1 Pencils of circles - inversive geometry -- §2 Cross-ratio -- §3 Möbius transformations, direct and reversed -- §4 Invariant points and classification of Möbius transformations -- §5 Complex distance of two pairs of points -- §6 Non-euclidean metric -- §7 Isometric transformations -- §8 Non-euclidean trigonometry -- §9 Products and commutators of motions -- Chapter II. Discontinuous groups of motions and reversions. -- §10 The concept of discontinuity -- §11 Groups with invariant points or lines -- §12 A discontinuity theorem -- §13 ℱ-groups. Fundamental set and limit set -- §14 The convex domain of an ℱ-group. Characteristic and isometric neighbourhood -- §15 Quasi-compactness modulo ℱ and finite generation of ℱ -- Chapter III. Surfaces associated with discontinuous groups. -- §16 The surfaces D modulo ℭ and K(ℱ) modulo ℱ -- §17 Area and type numbers -- Chapter IV. Decompositions of groups. -- §18 Composition of groups -- §19 Decomposition of groups -- §20 Decompositions of ℱ-groups containing reflections -- §21 Elementary groups and elementary surfaces -- §22 Complete decomposition and normal form in the case of quasi-compactness -- §23 Exhaustion in the case of non-quasi-compactness -- Chapter V. Isomorphism and homeomorphism. -- §24 Topological and geometrical isomorphism -- §25 Topological and geometrical homeomorphism -- §26 Construction of g-mappings. Metric parameters. Congruent groups -- Symbols and definitions -- Alphabets -- Bibliography -- Index |
| Record Nr. | UNINA-9910785820103321 |
|
Fenchel W (Werner), <1905->
|
||
| Berlin ; ; New York, : Walter de Gruyter, 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Discontinuous groups of isometries in the hyperbolic plane [[electronic resource] /] / Werner Fenchel, Jakob Nielsen ; edited by Asmus L. Schmidt
| Discontinuous groups of isometries in the hyperbolic plane [[electronic resource] /] / Werner Fenchel, Jakob Nielsen ; edited by Asmus L. Schmidt |
| Autore | Fenchel W (Werner), <1905-> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Berlin ; ; New York, : Walter de Gruyter, 2003 |
| Descrizione fisica | 1 online resource (388 p.) |
| Disciplina | 514/.2 |
| Altri autori (Persone) |
NielsenJakob <1890-1959.>
SchmidtAsmus L |
| Collana | De Gruyter studies in mathematics |
| Soggetto topico |
Discontinuous groups
Isometrics (Mathematics) |
| ISBN | 3-11-089135-2 |
| Classificazione | SK 380 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Chapter I. Möbius transformations and non-euclidean geometry. -- §1 Pencils of circles - inversive geometry -- §2 Cross-ratio -- §3 Möbius transformations, direct and reversed -- §4 Invariant points and classification of Möbius transformations -- §5 Complex distance of two pairs of points -- §6 Non-euclidean metric -- §7 Isometric transformations -- §8 Non-euclidean trigonometry -- §9 Products and commutators of motions -- Chapter II. Discontinuous groups of motions and reversions. -- §10 The concept of discontinuity -- §11 Groups with invariant points or lines -- §12 A discontinuity theorem -- §13 ℱ-groups. Fundamental set and limit set -- §14 The convex domain of an ℱ-group. Characteristic and isometric neighbourhood -- §15 Quasi-compactness modulo ℱ and finite generation of ℱ -- Chapter III. Surfaces associated with discontinuous groups. -- §16 The surfaces D modulo ℭ and K(ℱ) modulo ℱ -- §17 Area and type numbers -- Chapter IV. Decompositions of groups. -- §18 Composition of groups -- §19 Decomposition of groups -- §20 Decompositions of ℱ-groups containing reflections -- §21 Elementary groups and elementary surfaces -- §22 Complete decomposition and normal form in the case of quasi-compactness -- §23 Exhaustion in the case of non-quasi-compactness -- Chapter V. Isomorphism and homeomorphism. -- §24 Topological and geometrical isomorphism -- §25 Topological and geometrical homeomorphism -- §26 Construction of g-mappings. Metric parameters. Congruent groups -- Symbols and definitions -- Alphabets -- Bibliography -- Index |
| Record Nr. | UNINA-9910809760103321 |
|
Fenchel W (Werner), <1905->
|
||
| Berlin ; ; New York, : Walter de Gruyter, 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Elementary geometry in hyperbolic space [[electronic resource] /] / Werner Fenchel
| Elementary geometry in hyperbolic space [[electronic resource] /] / Werner Fenchel |
| Autore | Fenchel W (Werner), <1905-> |
| Edizione | [Reprint 2011] |
| Pubbl/distr/stampa | Berlin ; ; New York, : Walter de Gruyter, 1989 |
| Descrizione fisica | 1 online resource (240 p.) |
| Disciplina | 516.9 |
| Collana | De Gruyter Studies in Mathematics |
| Soggetto topico | Geometry, Hyperbolic |
| Soggetto genere / forma | Electronic books. |
| ISBN | 3-11-084945-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- I. Preliminaries -- II. The Möbius Group -- III. The Basic Notions of Hyperbolic Geometry -- IV. The Isometry Group of Hyperbolic Space -- V. Lines -- VI. Right-Angled Hexagons -- VII. Points and Planes -- VIII. Spherical Surfaces -- IX. Area and Volume -- References -- Index -- Backmatter |
| Record Nr. | UNINA-9910461927703321 |
|
Fenchel W (Werner), <1905->
|
||
| Berlin ; ; New York, : Walter de Gruyter, 1989 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Elementary geometry in hyperbolic space [[electronic resource] /] / Werner Fenchel
| Elementary geometry in hyperbolic space [[electronic resource] /] / Werner Fenchel |
| Autore | Fenchel W (Werner), <1905-> |
| Edizione | [Reprint 2011] |
| Pubbl/distr/stampa | Berlin ; ; New York, : Walter de Gruyter, 1989 |
| Descrizione fisica | 1 online resource (240 p.) |
| Disciplina | 516.9 |
| Collana | De Gruyter Studies in Mathematics |
| Soggetto topico | Geometry, Hyperbolic |
| ISBN | 3-11-084945-3 |
| Classificazione | SK 380 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- I. Preliminaries -- II. The Möbius Group -- III. The Basic Notions of Hyperbolic Geometry -- IV. The Isometry Group of Hyperbolic Space -- V. Lines -- VI. Right-Angled Hexagons -- VII. Points and Planes -- VIII. Spherical Surfaces -- IX. Area and Volume -- References -- Index -- Backmatter |
| Record Nr. | UNINA-9910785846503321 |
|
Fenchel W (Werner), <1905->
|
||
| Berlin ; ; New York, : Walter de Gruyter, 1989 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Elementary geometry in hyperbolic space [[electronic resource] /] / Werner Fenchel
| Elementary geometry in hyperbolic space [[electronic resource] /] / Werner Fenchel |
| Autore | Fenchel W (Werner), <1905-> |
| Edizione | [Reprint 2011] |
| Pubbl/distr/stampa | Berlin ; ; New York, : Walter de Gruyter, 1989 |
| Descrizione fisica | 1 online resource (240 p.) |
| Disciplina | 516.9 |
| Collana | De Gruyter Studies in Mathematics |
| Soggetto topico | Geometry, Hyperbolic |
| ISBN | 3-11-084945-3 |
| Classificazione | SK 380 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- I. Preliminaries -- II. The Möbius Group -- III. The Basic Notions of Hyperbolic Geometry -- IV. The Isometry Group of Hyperbolic Space -- V. Lines -- VI. Right-Angled Hexagons -- VII. Points and Planes -- VIII. Spherical Surfaces -- IX. Area and Volume -- References -- Index -- Backmatter |
| Record Nr. | UNINA-9910824478303321 |
|
Fenchel W (Werner), <1905->
|
||
| Berlin ; ; New York, : Walter de Gruyter, 1989 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||