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 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.
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 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.
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
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.