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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
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
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
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Author(s): NA
NA 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
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.
Author(s): Shalosh B. Ekhad
NA Pages
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.
Author(s): Theodore Shifrin
128 Pages
Differential Geometry and Physics
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Author(s): NA
NA Pages
Course of differential geometry
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NA Pages
Complex Analytic and Differential Geometry
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NA Pages
Functional Differential Geometry
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NA Pages
Quick Introduction to Tensor Analysis
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NA Pages
Introduction to Differential Forms
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