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Feb 9, 2023 at 8:07 comment added Ali Taghavi @AntonPetrunin Dear Anton Thank you for your kind attention to my question and your very helpful answer. BTW in the reference list of the book of Toendeur I had found a title of a paper some things like "on stability of Riemannian foliation" But I did not read the paper. Then I post this question here. Is your idea parallel to this paper mentioned in the (very long) bibliography of Tondeur book? How does orthogonality of leaf-geodesics relate to non existence of limit cycle?
Feb 8, 2023 at 21:53 comment added Anton Petrunin A closed leaf in a Riemannian foliation cannot have an asymptote.
Feb 8, 2023 at 21:17 history asked Ali Taghavi CC BY-SA 4.0