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Notes on Differential Geometry and Lie Groups
This note covers the following topics: Matrix Exponential; Some Matrix Lie Groups, Manifolds and Lie Groups, The Lorentz Groups, Vector Fields, Integral Curves, Flows, Partitions of Unity, Orientability, Covering Maps, The Log-Euclidean Framework, Spherical Harmonics, Statistics on Riemannian Manifolds, Distributions and the Frobenius Theorem, The Laplace-Beltrami Operator and Harmonic Forms, Bundles, Metrics on Bundles, Homogeneous Spaces, Cli ord Algebras, Cli ord Groups, Pin and Spin and Tensor Algebras.
Author(s): Jean Gallier
744 Pages 
Classical Differential Geometry Peter Petersen
This book explains the following topics: General Curve Theory, Planar Curves, Space Curves, Basic Surface Theory, Curvature of Surfaces, Surface Theory, Geodesics and Metric Geometry, Riemannian Geometry, Special Coordinate Representations.
Author(s): Peter Petersen
256 Pages
Differential Geometry in Toposes
This note explains the following topics: From Kock–Lawvere axiom to microlinear spaces, Vector bundles,Connections, Affine space, Differential forms, Axiomatic structure of the real line, Coordinates and formal manifolds, Riemannian structure, Well-adapted topos models.
Author(s): Ryszard Pawe Kostecki
93 Pages
Discrete Differential Geometry
This note covers the following topics: Discrete Curves, Curves and curvature, Flows on curves, Elastica, Darboux transforms, Discrete Surfaces, Abstract discrete surfaces, Polyhedral surfaces and piecewise flat surfaces, Discrete cotan Laplace operator, Delaunay tessellations, Line congruences over simplicial surfaces, Polyhedral surfaces with parallel Gauss map, Willmore energy.
Author(s): Alexander I. Bobenko
144 Pages
Elementary Differential Geometry Curves and Surfaces
The purpose of this course note is the study of curves and surfaces , and those are in general, curved. The book mainly focus on geometric aspects of methods borrowed from linear algebra; proofs will only be included for those properties that are important for the future development.
Author(s): Asst. Prof. Martin Raussen
160 Pages
Differential Geometry Of Three Dimensions
This book describes the fundamentals of metric differential geometry of curves and surfaces.
Author(s): C. E Weatherburn
280 Pages
Lecture Notes on Differential Geometry
This is a useful note for Differential Geometry. This note covers Curves, Surfaces and Manifolds
Author(s): Mohammad Ghomi
NA Pages