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.
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.
This
note contains on the following subtopics of Differential Geometry,
Manifolds, Connections and curvature, Calculus on
manifolds and Special topics.
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.
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.
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.
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
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.
Author(s): Ivan Kolar, Jan Slovak and Peter W. Michor
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.
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.