Hyperbolic Geometry
Seiten
2005
|
2nd ed. 2005
Springer London Ltd (Verlag)
978-1-85233-934-0 (ISBN)
Springer London Ltd (Verlag)
978-1-85233-934-0 (ISBN)
Featuring material on important topics such as hyperbolic geometry in higher dimensions and generalizations of hyperbolicity, this title includes full solutions for all exercises.
The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, providing the reader with a firm grasp of the concepts and techniques of this beautiful area of mathematics. Topics covered include the upper half-space model of the hyperbolic plane, Möbius transformations, the general Möbius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincaré disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications.
This updated second edition also features:
an expanded discussion of planar models of the hyperbolic plane arising from complex analysis;
the hyperboloid model of the hyperbolic plane;
a brief discussion of generalizations to higher dimensions;
many newexercises.
The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. This book provides a self-contained introduction to the subject, providing the reader with a firm grasp of the concepts and techniques of this beautiful area of mathematics. Topics covered include the upper half-space model of the hyperbolic plane, Möbius transformations, the general Möbius group and the subgroup preserving path length in the upper half-space model, arc-length and distance, the Poincaré disc model, convex subsets of the hyperbolic plane, and the Gauss-Bonnet formula for the area of a hyperbolic polygon and its applications.
This updated second edition also features:
an expanded discussion of planar models of the hyperbolic plane arising from complex analysis;
the hyperboloid model of the hyperbolic plane;
a brief discussion of generalizations to higher dimensions;
many newexercises.
The Basic Spaces.- The General Möbius Group.- Length and Distance in ?.- Planar Models of the Hyperbolic Plane.- Convexity, Area, and Trigonometry.- Nonplanar models.
| Erscheint lt. Verlag | 23.8.2005 |
|---|---|
| Reihe/Serie | Springer Undergraduate Mathematics Series |
| Zusatzinfo | 21 Illustrations, black and white; XII, 276 p. 21 illus. |
| Verlagsort | England |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 1-85233-934-9 / 1852339349 |
| ISBN-13 | 978-1-85233-934-0 / 9781852339340 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Gekrümmte Kurven und Flächen
Buch | Softcover (2024)
De Gruyter (Verlag)
CHF 76,90
Nielsen Methods, Covering Spaces, and Hyperbolic Groups
Buch | Softcover (2024)
De Gruyter (Verlag)
CHF 153,90
