MathOverflow is a question and answer site for professional mathematicians. 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

Let $G= \left\{ \begin{pmatrix} 1&a&c\\0&1&b\\0&0&0 \end{pmatrix} \mid a,b,c\in \mathbb{R} \right\}$ be the Heisenberg group. Is there a compact codimension one submanifold of $G$ which is totally geodesic? (We fix a left invariant metric for the Heisenberg group)

share|cite|improve this question
up vote 3 down vote accepted

The question is studied in detail in Pat Eberlein's 1994 paper. I believe the answer to your specific question is NO.

share|cite|improve this answer
thank you very much for your very interesting link. – Ali Taghavi Jul 6 '14 at 20:02

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.