A comprehensive introduction to differential geometry

@inproceedings{Spivak1975ACI,
  title={A comprehensive introduction to differential geometry},
  author={Michael David Spivak},
  year={1975}
}
Spivak's Comprehensive introduction takes as its theme the classical roots of contemporary differential geometry. Spivak explains his Main Premise (my term) as follows: "in order for an introduction to differential geometry to expose the geometric aspect of the subject, an historical approach is necessary; there is no point in introducing the curvature tensor without explaining how it was invented and what it has to do with curvature". His second premise concerns the manner in which the… 
The Riemann Curvature through history
The concept of curvature is very common in Differential Geometry. In this article we try to show its evolution along history, as well as some of its applications. This survey is limited both in
A Survey of the Development of Geometry up to 1870
This is an expository treatise on the development of the classical geometries, starting from the origins of Euclidean geometry a few centuries BC up to around 1870. At this time classical
New viewpoints in the geometry of submanifolds of $R^N$
0. Introduction. The geometry of submanifolds of euclidean space is the oldest branch of differential geometry. The subject was the original source of most of the classical and modern ideas in the
Aspects of Differential Geometry II
TLDR
The basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincare duality, and the Kunneth formula are proved, and a brief introduction to the theory of characteristic classes is given.
Applications of Affine and Weyl Geometry
TLDR
This book associates an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and uses this correspondence to study both geometries to be accessible to mathematicians who are not expert in the subject and to students with a basic grounding in differential geometry.
Differential Geometry: An Introduction to the Theory of Curves
Differential geometry is a discipline of mathematics that uses the techniques of calculus and linear algebra to study problems in geometry. The theory of plane, curves and surfaces in the Euclidean
ON DIFFERENTIABLE FIBRE BUNDLES : A CONCISE INTRODUCTION
This is a partial review of the connection theory on differentiable fibre bundles. From different view points, this theory can be found in many works, like [2–6, 9, 13–15, 18, 19, 24, 26, 27, 30, 31,
0 A ug 2 00 9 On the projective theory of sprays with applications to Finsler geometry Zoltán Szilasi
The origins. The basic ideas and structures of ‘modern differential geometry’ first appeared in Bernard Riemann’s habilitation lecture “Über die Hypothesen die der Geometrie zu Grunde liegen” (“On
...
...