Differential geometry
Date: 2014
Subject: curve
Frenet frame
curvature
torsion
hypersurface
fundamental forms
principal curvature
Gaussian curvature
Minkowski curvature
manifold
tensor field
connection
geodesic curve
K+F tárgyszavak::4 Élettelen természettudományok::4.5 Matematika
TÁMOP – 4.1.2-08/2/A/KMR
Frenet frame
curvature
torsion
hypersurface
fundamental forms
principal curvature
Gaussian curvature
Minkowski curvature
manifold
tensor field
connection
geodesic curve
K+F tárgyszavak::4 Élettelen természettudományok::4.5 Matematika
TÁMOP – 4.1.2-08/2/A/KMR
Abstract:
The aim of this textbook is to give an introduction to differential
geometry. It is based on the lectures given by the author at Eötvös
Loránd University and at Budapest Semesters in Mathematics. In the first
chapter, some preliminary definitions and facts are collected, that will be
used later. The classical roots of modern differential geometry are presented
in the next two chapters. Chapter 2 is devoted to the theory of curves,
while Chapter 3 deals with hypersurfaces in the Euclidean space. In the last
chapter, differentiable manifolds are introduced and basic tools of analysis
(differentiation and integration) on manifolds are presented. At the end of
Chapter 4, these analytical techniques are applied to study the geometry of
Riemannian manifolds.
