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Differential Geometry Books

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 Fernandes

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.

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s NAPages

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.

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s 93Pages

Introduction to Differential Geometry Lecture Notes

This note 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.

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s 160Pages

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):

s 225Pages

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.

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s 144Pages

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.

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s 160Pages

Differential Geometry Of Three Dimensions

This book describes the fundamentals of metric differential geometry of curves and surfaces.

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s 280Pages

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.

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s 281Pages

Lectures on Differential Geometry (PDF 221P)

This note contains on the following subtopics of Differential Geometry, Manifolds, Connections and curvature, Calculus on manifolds and Special topics.

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s 221Pages

Lecture Notes on Differential Geometry

This is a useful note for Differential Geometry. This note covers Curves, Surfaces and Manifolds

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s NAPages

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.

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s 225Pages

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.

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s 744Pages

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.

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s 64Pages

Geometry and linear algebra

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s NAPages

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.

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s 25Pages

Lecture Notes in Differential Geometry (PS)

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s NAPages

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.

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s NAPages

Plane Geometry

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.

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s NAPages

Natural operations in differential geometry

This 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.

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s 437Pages

Minimal surfaces in Euclidean spaces

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 Minimal Surfaces.

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s 72Pages

Differential Geometry Lecture Notes

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.

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s 49Pages

Differential Geometry A First Course in Curves and Surfaces

This 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.

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s 128Pages

Differential Geometry and Physics

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s NAPages

Course of differential geometry

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s NAPages

Complex Analytic and Differential Geometry

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s NAPages

Topics in Differential Geometry

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s NAPages

Functional Differential Geometry

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s NAPages

Differential Geometry Csikos B.

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s NAPages

Quick Introduction to Tensor Analysis

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s NAPages

Introduction to Differential Forms

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s NAPages

Complex Manifolds and Hermitian Differential Geometry

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s NAPages

Differential Geometry Reconstructed A Unified Systematic Framework

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s NAPages