3
$\begingroup$

Is there a compact orientable Riemannian manifold which does not have a compact totally geodesic submanifold of codimension $1$?

Improve this question
$\endgroup$

1 Answer 1

Reset to default
6
$\begingroup$

According to the answer of Petrunin https://mathoverflow.net/a/309692/121665, any metric on a 3-manifold admits arbitrary small $C^\infty$ deformation such that the obtained Riemannian manifold has no totally geodesic surfaces, even locally.

Improve this answer
$\endgroup$
1
  • $\begingroup$ Thank you very much for your answer. $\endgroup$
    – Ali Taghavi
    Apr 1, 2019 at 2:21

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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