Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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|improve this question

1 Answer 1

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

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.