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 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.
The purpose of this course note is the study of curves and surfaces ,
and those are in general, curved. The book mainly focus on geometric aspects of
methods borrowed from linear algebra; proofs will only be included for those
properties that are important for the future development.
This book is
addressed to the reader who wishes to cover a greater distance in a short time
and arrive at the front line of contemporary research. This book can serve as a
basis for graduate topics courses. Exercises play a prominent role while
historical and cultural comments relate the subject to a broader mathematical
context.
This
note contains on the following subtopics of Differential Geometry,
Manifolds, Connections and curvature, Calculus on
manifolds and Special topics.