Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

I don't know if this is an inappropriate question to post on stackexchange, but could somebody give me (reference me) a precise definition of "totally geodesic and flat submanifold" of a riemannian manifold?

Thank you!

share|cite|improve this question

Let $M$ be a Riemannian manifold. A submanifold $N$ of $M$ is totally geodesic if every geodesic in $N$ is also a geodesic in $M$. $N$ is flat if its curvature vanishes.

Let me know if there is anything above that you would like further clarification on.

share|cite|improve this answer

Your Answer

 
discard

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.