Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

DIRECT SUM FOR BASIC COHOMOLOGY OF CODIMENSION FOUR TAUT RIEMANNIAN FOLIATION

  • Zhou, Jiuru (School of Mathematical Sciences Yangzhou University)
  • Received : 2020.01.07
  • Accepted : 2020.06.04
  • Published : 2020.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

We discuss the decomposition of degree two basic cohomology for codimension four taut Riemannian foliation according to the holonomy invariant transversal almost complex structure J, and show that J is C∞ pure and full. In addition, we obtain an estimate of the dimension of basic J-anti-invariant subgroup. These are the foliated version for the corresponding results of T. Draghici et al. [3].

Keywords

References

  1. D. Dominguez, Finiteness and tenseness theorems for Riemannian foliations, Amer. J. Math. 120 (1998), no. 6, 1237-1276. https://doi.org/10.1353/ajm.1998.0048
  2. S. K. Donaldson, Two-forms on four-manifolds and elliptic equations, in Inspired by S. S. Chern, 153-172, Nankai Tracts Math., 11, World Sci. Publ., Hackensack, NJ, 2006. https://doi.org/10.1142/9789812772688_0007
  3. T. Draghici, T.-J. Li, and W. Zhang, Symplectic forms and cohomology decomposition of almost complex four-manifolds, Int. Math. Res. Not. IMRN 2010, no. 1, 1-17. https://doi.org/10.1093/imrn/rnp113
  4. A. Fino and A. Tomassini, On some cohomological properties of almost complex manifolds, J. Geom. Anal. 20 (2010), no. 1, 107-131. https://doi.org/10.1007/s12220-009-9098-3
  5. F. W. Kamber and P. Tondeur, Foliations and metrics, in Differential geometry (College Park, Md., 1981/1982), 103-152, Progr. Math., 32, Birkhauser Boston, Boston, MA, 1983.
  6. F. W. Kamber and P. Tondeur, Duality for Riemannian foliations, in Singularities, Part 1 (Arcata, Calif., 1981), 609-618, Proc. Sympos. Pure Math., 40, Amer. Math. Soc., Providence, RI, 1983.
  7. T.-J. Li and W. Zhang, Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom. 17 (2009), no. 4, 651-683. https://doi.org/10.4310/CAG.2009.v17.n4.a4
  8. J. A. A. Lopez, The basic component of the mean curvature of Riemannian foliations, Ann. Global Anal. Geom. 10 (1992), no. 2, 179-194. https://doi.org/10.1007/BF00130919
  9. P. Tondeur, Geometry of foliations, Monographs in Mathematics, 90, Birkhauser Verlag, Basel, 1997. https://doi.org/10.1007/978-3-0348-8914-8
  10. J. Zhou and P. Zhu, Basic cohomology group decomposition of K-contact 5-manifolds, Results Math. 71 (2017), no. 3-4, 1023-1030. https://doi.org/10.1007/s00025-016-0559-2