Differential Geometry of Curves and Surfaces / Springer Undergraduate Mathematics Series (PDF)
There are five chapters: 1. Plane Curves and Space...
- Lastschrift, Kreditkarte, Paypal, Rechnung
- Kostenloser tolino webreader
There are five chapters: 1. Plane Curves and Space Curves; 2. Local Theory of Surfaces in Space; 3. Geometry of Surfaces; 4. Gauss-Bonnet Theorem; and 5. Minimal Surfaces.
Chapter 1 discusses local and global properties of planar curves and curves in space. Chapter 2 deals with local properties of surfaces in 3-dimensional Euclidean space. Two types of curvatures - the Gaussian curvature K and the mean curvature H -are introduced. The method of the moving frames, a standard technique in differential geometry, is introduced in the context of a surface in 3-dimensional Euclidean space. In Chapter 3, the Riemannian metric on a surface is introduced and properties determined only by the first fundamental form are discussed. The concept of a geodesic introduced in Chapter 2 is extensively discussed, and several examples of geodesics are presented with illustrations. Chapter 4 starts with a simple and elegant proof of Stokes' theorem for a domain. Then the Gauss-Bonnet theorem, the major topic of this book, is discussed at great length. The theorem is a most beautiful and deep result in differential geometry. It yields a relation between the integral of the Gaussian curvature over a given oriented closed surface S and the topology of S in terms of its Euler number ¿(S). Here again, many illustrations are provided to facilitate the reader's understanding. Chapter 5, Minimal Surfaces, requires some elementary knowledge of complex analysis. However, the author retained the introductory nature of this book and focused on detailed explanations of the examples of minimal surfaces given in Chapter 2.
- Autor: Shoshichi Kobayashi
- 2019, 1st ed. 2019, 192 Seiten, Englisch
- Übersetzer: Eriko Shinozaki Nagumo, Makiko Sumi Tanaka
- Verlag: Springer-Verlag GmbH
- ISBN-10: 9811517398
- ISBN-13: 9789811517396
- Erscheinungsdatum: 13.11.2019
Abhängig von Bildschirmgröße und eingestellter Schriftgröße kann die Seitenzahl auf Ihrem Lesegerät variieren.
- Dateiformat: PDF
- Größe: 2.88 MB
- Ohne Kopierschutz
- Vorlesefunktion
Schreiben Sie einen Kommentar zu "Differential Geometry of Curves and Surfaces / Springer Undergraduate Mathematics Series".
Kommentar verfassen