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Projective differential geometry old and new from Schwarzian derivative to cohomology of diffeomorphism groups
This book is addressed to the reader who wishes to cover a greater distance in a short time and arrive at the front line of contemporary research. This book can serve as a basis for graduate topics courses. Exercises play a prominent role while historical and cultural comments relate the subject to a broader mathematical context.
Author(s): Ovsienko and Tabachnikov
281 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
An Introduction to Differential Geometry through Computation
This note explains the following topics: Linear Transformations, Tangent Vectors, The push-forward and the Jacobian, Differential One-forms and Metric Tensors, The Pullback and Isometries, Hypersurfaces, Flows, Invariants and the Straightening Lemma, The Lie Bracket and Killing Vectors, Hypersurfaces, Group actions and Multi-parameter Groups, Connections and Curvature.
Author(s): Mark E. Fels
225 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
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
Lectures on Symplectic Geometry (PDF 225P)
This note contains on the following subtopics of Symplectic Geometry, Symplectic Manifolds, Symplectomorphisms, Local Forms, Contact Manifolds, Compatible Almost Complex Structures, Kahler Manifolds, Hamiltonian Mechanics, Moment Maps, Symplectic Reduction, Moment Maps Revisited and Symplectic Toric Manifolds.
Author(s): Ana Cannas da Silva
225 Pages
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
Notes on Differential Geometry
These notes are an attempt to summarize some of the key mathematical aspects of differential geometry,as they apply in particular to the geometry of surfaces in R3. Covered topics are: Some fundamentals of the theory of surfaces, Some important parameterizations of surfaces, Variation of a surface, Vesicles, Geodesics, parallel transport and covariant differentiation.
Author(s): Markus Deserno
64 Pages
Notes on Differential Geometry, Lars Andersson 1
This note covers the following topics: Linear Algebra, Differentiability, integration, Cotangent Space, Tangent and Cotangent bundles, Vector fields and 1 forms, Multilinear Algebra, Tensor fields, Flows and vectorfields, Metrics.
Author(s): Lars Andersson
25 Pages
Natural Operations in Differential Geometry
This book is a monographical work on natural bundles and natural operators in differential geometry and this book tries to be a rather comprehensive textbook on all basic structures from the theory of jets which appear in different branches of differential geometry.
Author(s): Ivan Kolar, Jan Slovak and Peter W. Michor
NA Pages
Course of differential geometry
Currently this section contains no detailed description for the page, will update this page soon.
Author(s): NA
NA Pages
Complex Analytic and Differential Geometry
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Author(s): NA
NA Pages
Functional Differential Geometry
Currently this section contains no detailed description for the page, will update this page soon.
Author(s): NA
NA Pages
Quick Introduction to Tensor Analysis
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Author(s): NA
NA Pages
Introduction to Differential Forms
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Author(s): NA
NA Pages
Complex Manifolds and Hermitian Differential Geometry
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Author(s): NA
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