DOI QR코드

DOI QR Code

UNIT TANGENT SPHERE BUNDLES OF TWO-POINT HOMOGENEOUS SPACES

  • 투고 : 2019.01.28
  • 심사 : 2019.03.08
  • 발행 : 2019.09.25

초록

We characterize two-point homogeneous spaces M by means of the structural operator $h={\frac{1}{2}}{\mathcal{L}}_{\xi}{\phi}$ or the characteristic Jacobi operator ${\ell}=R({\cdot},{\xi}){\xi}$ on the unit tangent sphere bundles $T_1M$.

키워드

참고문헌

  1. J. Berndt and L. Vanhecke, Two natural generalizations of locally symmetric spaces, Diffential Geom. Appl. 2 (1992), 57-80. https://doi.org/10.1016/0926-2245(92)90009-C
  2. D. E. Blair, Critical associated metrics on contact manifolds III, J. Austral. Math. Soc. 50 (1991), 189-196. https://doi.org/10.1017/S1446788700032675
  3. D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Second edition, Progr. Math. 203, Birkhauser Boston, Inc., Boston, MA, 2010.
  4. E. Boeckx, J. T. Cho and S. H. Chun, Flow-invariant structures on unit tangent sphere bundles, Publ. Math. Debrecen 70 (2007), 167-178.
  5. E. Boeckx, D.Perrone and L.Vanhecke, Unit tangent sphere bundles and two-point homogeneous spaces, Periodica Math. Hungarica 36 (1998), 79-95. https://doi.org/10.1023/A:1004629423529
  6. E. Boeckx and L.Vanhecke, Characteristic reflections on unit tangent sphere bundles, Houston J. Math. 23 (1997), 427-448.
  7. E. Cartan, Geometry of Riemannian spaces, Math. Sci. Press, Brooklyn, Mass., 1983.
  8. J. T. Cho and S. H. Chun, On the classification of contact Riemannian manifolds satisfying the condition (C), Glasgow Math. J. 45 (2003), 99-113.
  9. J. T. Cho and S. H. Chun, The unit tangent sphere bundle of a complex space form, J. Korean Math. Soc. 41 (2004), 1035-1047. https://doi.org/10.4134/JKMS.2004.41.6.1035
  10. J. T. Cho and S. H. Chun, Reeb flow invariant unit tangent sphere bundles, Honam Math. J. 36(4) (2014), 805-812. https://doi.org/10.5831/HMJ.2014.36.4.805
  11. J. T. Cho and S. H. Chun, Pseudo-symmetry on unit tangent sphere bundles, Honam Math. J. 38(2) (2016), 375-384. https://doi.org/10.5831/HMJ.2016.38.2.375
  12. P. Dombrowski, On the geometry of the tangent bundle, J. Reine Angew. Math. 210 (1962), 73-88.
  13. P. Gilkey, A. Swann and L. Vanhecke, Isoparametric geodesic spheres and a conjecture of Osserman concerning the Jacobi operator, Quart. J. Math. Oxford 46 (1995), 299-320. https://doi.org/10.1093/qmath/46.3.299
  14. O. Kowalski, Curvature of the induced Riemannian metric of the tangent bundle of a Riemannian manifold, J. Reine Angew. Math. 250 (1971), 124-129.
  15. D. Perrone, Torsion tensor and critical metrics on contact (2n + 1)-manifolds, Monatsh. Math. 114 (1992), 245-259. https://doi.org/10.1007/BF01299383
  16. D. Perrone, Tangent sphere bundles satisfying ${\nabla}_{\xi}{\tau}$ = 0, J. Geom. 49 (1994), 178-188. https://doi.org/10.1007/BF01228060
  17. Y. Tashiro, On contact structures of unit tangent sphere bundles, Tohoku Math. J. 21 (1969), 117-143. https://doi.org/10.2748/tmj/1178243040
  18. K. Yano and S. Ishihara, Tangent and cotangent bundles M. Dekker Inc., 1973.