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.
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.
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.