First Steps in Differential Geometry

Riemannian, Contact, Symplectic

  • Andrew¬†McInerney

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Andrew McInerney
    Pages 1-7
  3. Andrew McInerney
    Pages 9-66
  4. Andrew McInerney
    Pages 67-133
  5. Andrew McInerney
    Pages 135-193
  6. Andrew McInerney
    Pages 195-270
  7. Andrew McInerney
    Pages 271-337
  8. Andrew McInerney
    Pages 339-404
  9. Back Matter
    Pages 405-410

About this book


Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view.

This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.


Riemannian geometry contact geometry differential forms differential geometry symplectic geometry tensors

Authors and affiliations

  • Andrew¬†McInerney
    • 1
  1. 1.City University of New York, Dept. of Mathematics and Computer SciencBronx Community CollegeBronxUSA

Bibliographic information