Synthetic Geometry of Manifolds
by Anders Kock
Publisher: University of Aarhus 2009
Number of pages: 314
This textbook can be used as a non-technical and geometric gateway to many aspects of differential geometry. The audience of the book is anybody with a reasonable mathematical maturity, who wants to learn some differential geometry.
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by Jonathan Holland, Bogdan Ion - arXiv
Contents: Affine connections and transformations; Symmetric spaces; Orthogonal symmetric Lie algebras; Examples; Noncompact symmetric spaces; Compact semisimple Lie groups; Hermitian symmetric spaces; Classification of real simple Lie algebras.
by Aleks Kleyn, Alexandre Laugier - arXiv
In this paper, we considered the definition of orthonormal basis in Minkowski space, the structure of metric tensor relative to orthonormal basis, procedure of orthogonalization. Contents: Preface; Minkowski Space; Examples of Minkowski Space.
by Anders Kock - Cambridge University Press
Synthetic differential geometry is a method of reasoning in differential geometry and calculus. This book is the second edition of Anders Kock's classical text, many notes have been included commenting on new developments.
by J.L. Koszul - Tata Institute of Fundamental Research
From the table of contents: Differential Calculus; Differentiable Bundles; Connections on Principal Bundles; Holonomy Groups; Vector Bundles and Derivation Laws; Holomorphic Connections (Complex vector bundles, Almost complex manifolds, etc.).