Introduction
Differential Geometry is a fascinating field of mathematics that studies the geometry of smooth shapes and spaces, known as smooth manifolds. It combines techniques from differential calculus, integral calculus, linear algebra, and multilinear algebra to explore these structures.
Contents
Extrinsic Geometry of
Differentiable Curves
Regular Surfaces
Geodesic and Geodesic Curvature
Geometry of Manifolds
Differential Calculus
Manifolds, Atlases and Smooth Structures
Smooth Functions and Maps
Tangent Vectors and Spaces
Vector Bundles
Partitions of Unity
Vector Fields and Lie Algebra
Lie Groups
Integral Curves and Flows
Distributions and Foliations
Differential Forms
Integration of Differential Forms
de Rham Cohomology
Tensor Fields
Connections
More …
References and Useful Resources
Ben Andrews, Lectures on Differential Geometry
Manfredo P. do Carmo, Differential Geometry of Curves and Surfaces.
Introduction to Differential Geometry.