This book
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 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.
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.