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Compact leaves of the foliation defined by the kernel of a T²-invariant presymplectic form.
- Source :
- Mathematical Journal of Ibaraki University; 2022, Vol. 54, p1-10, 10p
- Publication Year :
- 2022
-
Abstract
- We investigate the foliation defined by the kernel of an exact presymplectic form dα of rank 2n on a (2n + r)-dimensional closed manifold M. For r = 2, we prove that the foliation has at least two leaves which are homeomorphic to a 2-dimensional torus, if M admits a locally free T²-action which preserves dα and satisfies that the function α(Z<subscript>2</subscript>) is constant, where Z<subscript>1</subscript>,Z<subscript>2</subscript> are the infinitesimal generators of the T²-action. We also give its generalization for r ≥ 1. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 13433636
- Volume :
- 54
- Database :
- Complementary Index
- Journal :
- Mathematical Journal of Ibaraki University
- Publication Type :
- Academic Journal
- Accession number :
- 162912135
- Full Text :
- https://doi.org/10.5036/mjiu.54.1