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.
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