This section contains free e-books and guides on Differential Geometry, some of the resources in this section can be viewed online and some of them can be downloaded.
Differential Geometry by Rui Loja FernandesRui Loja FernandesOnline
| NA Pages
This note covers
the following topics: Manifolds as subsets of Euclidean space, Abstract
Manifolds, Tangent Space and the Differential, Embeddings and Whitney’s Theorem,
The de Rham Theorem, Lie Theory, Differential Forms, Fiber Bundles.
Differential Geometry in ToposesRyszard Pawe KosteckiPDF
| 93 Pages
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.
Introduction to Differential Geometry Lecture NotesEckhard MeinrenkenPDF
| 160 Pages
covers the following topics: Manifolds, Oriented manifolds, Compact subsets,
Smooth maps, Smooth functions on manifolds, The tangent bundle, Tangent spaces,
Vector field, Differential forms, Topology of manifolds, Vector bundles.
An Introduction to Differential Geometry through ComputationMark E. FelsPDF
| 225 Pages
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.
Discrete Differential GeometryAlexander I. BobenkoPDF
| 144 Pages
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.
Elementary Differential Geometry Curves and SurfacesAsst. Prof. Martin
| 160 Pages
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.
Lectures on Differential Geometry (PDF 221P)Wulf RossmannPDF
| 221 Pages
note contains on the following subtopics of Differential Geometry,
Manifolds, Connections and curvature, Calculus on
manifolds and Special topics.
Lectures on Symplectic Geometry (PDF 225P)Ana Cannas
| 225 Pages
This note contains on the following subtopics
of Symplectic Geometry, Symplectic Manifolds,
Forms, Contact Manifolds, Compatible Almost Complex Structures, Kahler
Manifolds, Hamiltonian Mechanics, Moment Maps, Symplectic Reduction, Moment Maps
Revisited and Symplectic Toric Manifolds.
Notes on Differential Geometry and Lie GroupsJean GallierPDF
| 744 Pages
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.
Notes on Differential GeometryMarkus DesernoPDF
| 64 Pages
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
|Geometry and linear algebra|
Notes on Differential Geometry, Lars Andersson 1Lars AnderssonPDF
| 25 Pages
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.
|Lecture Notes in Differential Geometry (PS)|
Natural Operations in Differential GeometryIvan
Kolar, Jan Slovak and Peter W. MichorOnline
| NA Pages
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.
Plane GeometryShalosh B. EkhadOnline
| NA Pages
This book explains about following
theorems in Plane Geometry: Brianchon's Theorem, Carnot's Theorem, Centroid
Exists Theorem, Ceva's Theorem, Clifford's Theorem, Desargues's Theorem, Euler
Line Exists Theorem, Feuerbach's Theorem, The Finsler-Hadwiger Theorem,
Fregier's Theorem, Fuhrmann's Theorem, Griffiths's Theorem, Incenter Exists
Theorem, Lemoine's Theorem, Ptolemy's Theorem.
Natural operations in differential geometryIvan Kolar, Jan Slovak and Peter W. MichorOnline
| 437 Pages
book covers the following topics: Manifolds And Lie Groups, Differential Forms,
Bundles And Connections, Jets And Natural Bundles, Finite Order Theorems,
Methods For Finding Natural Operators, Product Preserving Functors, Prolongation
Of Vector Fields And Connections, General Theory Of Lie Derivatives.
Minimal surfaces in Euclidean spacesMatthias WeberPDF
| 72 Pages
This book covers
the following topics: Basic Differential Geometry Of
Surfaces, The Weierstrass Representation, Minimal surfaces on Punctured Spheres,
The Scherk Surfaces, Minimal Surfaces Defined On Punctured Tori, Higher Genus
Differential Geometry Lecture NotesDmitri
| 49 Pages
This book covers the following topics: Smooth Manifolds, Plain curves, Submanifolds, Differentiable maps, immersions,
submersions and embeddings, Basic results from Differential Topology, Tangent
spaces and tensor calculus, Riemannian geometry.
Differential Geometry A First Course in Curves and SurfacesTheodore ShifrinPDF
| 128 Pages
note covers the following topics: Curves, Surfaces: Local Theory, Holonomy and
the Gauss-Bonnet Theorem, Hyperbolic Geometry, Surface Theory with Differential
Forms, Calculus of Variations and Surfaces of Constant Mean Curvature.
|Differential Geometry and Physics|
|Course of differential geometry |
|Complex Analytic and Differential Geometry|
|Topics in Differential Geometry|
|Functional Differential Geometry|
|Differential Geometry Csikos B.|
|Quick Introduction to Tensor Analysis|
|Introduction to Differential Forms|
|Complex Manifolds and Hermitian Differential Geometry|
|Differential Geometry Reconstructed A Unified Systematic Framework|