Abstract
For K-contact flows on (2n+1)-dimensional compact manifolds, we show that the dimension of any leaf closure is at most the smaller of (n+1) and 2n+1) minus the rank of the vector space of harmonic vector fields.
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References
Blair, D.:Contact manifolds in riemannian geometry. Lecture Notes in Math.509, Springer Verlag, Berlin and New York 1976.
Carriere, Y.: Flots riemanniens. In: Structures Transverses des Feuilletages.Astérisque 116 (1984), 31–52.
Dieck, T.:Transformation groups. Walter de Gruyter, Berlin, New York 1987.
Molino, P.:Riemannian foliations. Progress in Mathematics, Birkhäuser, Boston 1984.
Molino, P.: Réduction symplectique et feuilletages riemanniens; moment structural et théorème de convexité. In:Séminaire Gaston Darboux de Géometrie et Topologie Différentielle 1987–1988. Univ. of Montpellier, 11–25.
Mosgawa, W.: Feuilletages de Killing.Collect. Math. 36 (1985), 285–290.
Rukimbira, P.: Some remarks on R-contact flows.Ann. Global Anal. Geom. 11 (1993), 165–171.
Rukimbira, P.:R-contactness and Chern-Hamilton's conjecture. Preprint.
Tachibana, S.: On harmonic tensors in compact Sasakian spaces.Tôhoku Math. J. 17 (1965), 271–284.
Viterbo, C.: A proof of Weinstein Conjecture in R2n.Ann. Inst. H. Poincaré Anal. Non Linéaire 4 (1987), 337–356.
Wadsley, A.W.: Geodesic foliations by circles.J. Differential Geom. 10 (1975), 541–549.
Weinstein, A.: On the hypothesis of Rabinowitz's periodic orbits theorem.J. Differential Equations 33 (1978), 353–358.
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Rukimbira, P. The dimension of leaf closures of K-contact flows. Ann Glob Anal Geom 12, 103–108 (1994). https://doi.org/10.1007/BF02108291
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DOI: https://doi.org/10.1007/BF02108291