# Book Details

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Preface | Table of Contents | MARC record | Metadata XML | e-Book PDF (2429 KB)*Iskander A. Taimanov (Sobolev Institute of Mathematics, Novosibirsk, Russia)*

#### Lectures on Differential Geometry

ISBN print 978-3-03719-050-0, ISBN online 978-3-03719-550-5DOI 10.4171/050

April 2008, 219 pages, softcover, 17.0 x 24.0 cm.

34.00 Euro

Differential geometry studies geometrical objects using analytical methods.
Like modern analysis itself, differential geometry originates in classical
mechanics. For instance, geodesics and minimal surfaces are defined via
variational principles and the curvature of a curve is easily interpreted as
the acceleration with respect to the path length parameter. Modern
differential geometry in its turn strongly contributed to modern physics.

This book gives an introduction to the basics of differential geometry, keeping
in mind the natural origin of many geometrical quantities, as well as
the applications of differential geometry and its methods to other sciences.

The text is divided into three parts. The first part covers the basics of curves
and surfaces, while the second part is designed as an introduction to smooth
manifolds and Riemannian geometry. In particular, Chapter 5 contains short
introductions to hyperbolic geometry and geometrical principles of special
relativity theory. Here, only a basic knowledge of algebra, calculus and ordinary
differential equations is required. The third part is more advanced and
introduces into matrix Lie groups and Lie algebras, representation theory of
groups, symplectic and Poisson geometry, and applications of complex analysis
in surface theory.

The book is based on lectures the author held repeatedly at Novosibirsk State
University. It is addressed to students as well as to anyone who wants to learn
the basics of differential geometry.

*Keywords: *Differential geometry, Riemannian geometry, smooth manifolds, minimal surfaces, Lie groups, representation theory, symplectic and Poisson geometry, finite-dimensional integrable systems