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Record Nr. |
UNINA9910462018803321 |
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Autore |
Fenchel W (Werner), <1905-> |
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Titolo |
Discontinuous groups of isometries in the hyperbolic plane [[electronic resource] /] / Werner Fenchel, Jakob Nielsen ; edited by Asmus L. Schmidt |
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Pubbl/distr/stampa |
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Berlin ; ; New York, : Walter de Gruyter, 2003 |
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ISBN |
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Descrizione fisica |
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1 online resource (388 p.) |
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Collana |
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De Gruyter studies in mathematics ; ; 29 |
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Altri autori (Persone) |
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NielsenJakob <1890-1959.> |
SchmidtAsmus L |
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Disciplina |
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Soggetti |
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Discontinuous groups |
Isometrics (Mathematics) |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (p. [355]-359) and index. |
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Nota di contenuto |
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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 |
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