02786nam a22003615a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016707200150018408400150019910000360021424500850025026000820033530000340041733600260045133700260047733800360050334700240053949000610056350600660062452015320069065000470222265000240226965000310229385600320232485600680235676-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20080408sz fot ||| 0|eng d a978303719550570a10.4171/0502doi ach0018173 7aPBMP2bicssc 7aPB2bicssc a53-xx2msc1 aTaimanov, Iskander A.,eauthor.10aLectures on Differential Geometryh[electronic resource] /cIskander A. Taimanov3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2008 a1 online resource (219 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Series of Lectures in Mathematics (ELM) ;x2523-51761 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aDifferential 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.07aDifferential & Riemannian geometry2bicssc07aMathematics2bicssc07aDifferential geometry2msc40uhttps://doi.org/10.4171/050423cover imageuhttps://www.ems-ph.org/img/books/taimanov_mini.jpg