We prove that the set of leaves of a singular foliation with the Nishimori relation is partially ordered if and only if all leaves are proper.
Similar content being viewed by others
References
I. Tamura, Topology of Foliations: An Introduction, Am. Math. Soc., Providence, RI (1992).
V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer, New York etc. (1989).
H. Sussmann, “Orbits of families of vector fields and integrability of systems with singularities,” Bull. Am. Math. Soc. 79, 197–199 (1973).
H. Sussmann, “Orbits of families of vector fields and integrability of distribution,” Trans. Am. Math. Soc. 180, 171–188 (1973).
A. Azamov and A. Narmanov, “On the limit sets of orbits of systems of vector fields,” Differ. Equ. 40, No. 2, 271–275 (2004).
P. Stefan, “ Accessibility and foliations with singularities,” Bull. Am. Math. Soc. 80, 1142–1145 (1974).
P. Stefan, “ Accessible sets, orbits, and foliations with singularities,” Proc. Lond. Math. Soc., III. Ser. 29, 699–713 (1974).
A. Ya. Narmanov, “On limit sets of leaves of a foliation of codimension 1,” Vestn. Leningr. Univ., Math. 16, 163–168 (1984).
T. Nishimori, “Behaviour of leaves of codimension-one foliations,” Tohoku Math. J, II. Ser. 29, 255–273 (1977).
Author information
Authors and Affiliations
Corresponding author
Additional information
International Mathematical Schools. Vol. 6. Mathematical Schools in Uzbekistan
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Narmanov, A. Topology of Singular Foliations. J Math Sci 277, 439–445 (2023). https://doi.org/10.1007/s10958-023-06847-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-023-06847-7