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.
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.
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
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.
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.
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.