MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Is there a detailed treatment of differential geometry using Robinson's infinitesimals?

share|cite|improve this question
Since you specified Robinson, you might not be interested in the other type of infinitesimals (nilpotent). But Models for Smooth Infinitesimal Analysis by Moerdijk and Reyes treats a number of topics in differential geometry (using both invertible and nilpotent infinitesimals, but mainly the latter). – Todd Trimble Apr 2 '13 at 12:33
Differential geometry using the infinitesimals Todd mentions is known as synthetic differential geometry: There are a couple of online textbooks by Anders Kock listed there. – David Corfield Apr 2 '13 at 14:47

I'm not aware of much. But two works worth noting are:

K.G. Schlesinger. Generalized Manifolds. Chapman & Hall/CRC, 1997.

I.O. Hamad. Generalized curvature and torsion in nonstandard analysis. PhD thesis, Salahaddin University - Erbil, 2007.

share|cite|improve this answer

Somewhat belatedly we developed foundations for differential geometry using infinitesimal displacements here:

Nowik, T.; Katz, M. "Differential geometry via infinitesimal displacements." Journal of Logic and Analysis 7:5 (2015), 1-44.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.