Honam Mathematical Journal (호남수학학술지)

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HOMOGENEOUS STRUCTURES ON CONTACT HYPERSURFACES IN HERMITIAN SYMMETRIC SPACES

  • Jong Taek, Cho (Department of Mathematics, Chonnam National University)
  • Received : 2022.09.16
  • Accepted : 2022.10.21
  • Published : 2022.12.25
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Abstract

We find a 1-parameter family of homogeneous structure tensors on contact hypersurfaces in Hermitian symmetric spaces. Among their associated Ambrose-Singer connections, we prove that the TanakaWebster connection is the unique pseudo-homothetically invariant connection.

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References

  1. W. Ambrose and I. M. Singer, On homogeneous Riemannian manifolds, Duke Math. J. 25 (1958), 647-669. https://doi.org/10.1215/S0012-7094-58-02560-2
  2. J. Berndt and Y. J. Suh, Contact hypersurfaces in Kahler manifolds, Proc. Amer. Math. Soc. 142 (2014), 2637-2649.
  3. D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Second edition, Progress in Math. 203, Birkhauser Boston, Inc., Boston, 2010.
  4. D. E. Blair, T. Koufogiorgos and B.J. Papantoniou, Contact metric manifolds satisfying a nullity condition, Israel J. Math. 91 (1995), 189-214. https://doi.org/10.1007/BF02761646
  5. E. Boeckx, A class of locally φ-symmetric contact metric spaces, Arch. Math. 72 (1999), 466-472. https://doi.org/10.1007/s000130050357
  6. E. Boeckx, A full classification of contact metric (k, µ)-spaces, Illinoise J. Math. 44 (2005), 275-285.
  7. E. Boeckx and J. T. Cho, Pseudo-Hermitian symmetries, Israel J. Math. 166 (2008), 125-145. https://doi.org/10.1007/s11856-008-1023-0
  8. J. T. Cho, Contact hypersurfaces and CR-symmetry, Ann. Mat. Pura Appl. 199 (2020), 1873-1884. https://doi.org/10.1007/s10231-020-00946-x
  9. S. Dragomir and G. Tomassini, Differential geometry and analysis on CR manifolds, Progr. Math. 246, Birkhauser Boston, Inc., Boston, MA, 2006.
  10. J. Gray, Some global properties of contact structure, Ann. of Math. 69 (1959), 421-450. https://doi.org/10.2307/1970192
  11. V. F. Kiricenko, On homogeneous Riemannian spaces with invariant tensor structure, Soviet Math. Dokl. 21 (1980), 734-747.
  12. S. Klein and Y. J. Suh, Contact real hypersurfaces in the complex hyperbolic quadric, Ann. Mat. Pura Appl. 198 (2019), 1481-1494. https://doi.org/10.1007/s10231-019-00827-y
  13. S. Sasaki, On differential manifolds with certain structures which are closely related to almost contact structure I, Tˆohoku Math J. 12 (1960), 456-476.
  14. N. Tanaka, On non-degenerate real hypersurfaces, grade Lie algebras and Cartan connections, Japan J. Math. 2 (1976), 131-190. https://doi.org/10.4099/math1924.2.131
  15. S. Tanno, The topology of contact Riemannian manifolds, Illinois J. Math. 12 (1968), 700-717. https://doi.org/10.1215/ijm/1256053971
  16. S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc. 314 (1989), 349-379. https://doi.org/10.1090/S0002-9947-1989-1000553-9
  17. F. Tricerri and L. Vanhecke, Homogeneous Structures on Riemannian Manifolds, Lecture Notes Series, London Math. Soc. 52, Cambridge Univ. Press, 1983.
  18. S. M. Webster, Pseudo-Hermitian structures on a real hypersurface, J. Differential Geom. 13 (1978), 25-41.