explains the following topics: General Curve Theory, Planar Curves, Space
Curves, Basic Surface Theory, Curvature of Surfaces, Surface Theory, Geodesics
and Metric Geometry, Riemannian Geometry, Special Coordinate Representations.
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,
Forms, Contact Manifolds, Compatible Almost Complex Structures, Kahler
Manifolds, Hamiltonian Mechanics, Moment Maps, Symplectic Reduction, Moment Maps
Revisited and Symplectic Toric Manifolds.
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.
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.