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Kniha Introduction to Differential Geometry Joel W. Robbin

Introduction to Differential Geometry

Autor: Joel W. Robbin, Dietmar A. Salamon
Jazyk: Angličtina
Vazba: Brožovaná
Vydavatel: Springer Fachmedien Wiesbaden
Dostupnost: Skladem u dodavatele
Odesíláme za 10-18 dnů
954 Kč
This textbook is suitable for a one semester lecture course on differential geometry for students of...

Informace o knize

Autor
Joel W. Robbin, Dietmar A. Salamon
Jazyk
Angličtina
Vazba
Kniha - Brožovaná
Vydáno
2022
Stránek
418
EAN
9783662643396
ISBN
3662643391
Enbook ID
38447681
Vydavatel
Springer Fachmedien Wiesbaden
Hmotnost
658
Rozměry
155 x 235 x 24

Kompletní popis

This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point.The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor.An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.

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