Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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PSEUDO-HERMITIAN 2-TYPE LEGENDRE SURFACES IN THE UNIT SPHERE S5

  • Lee, Ji-Eun (Institute of Basic Science Chonnam National University)
  • Received : 2018.12.21
  • Accepted : 2019.08.02
  • Published : 2020.01.31
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Abstract

In this paper, we show that it is Chen surfaces that non-minimal pseudo-Hermitian mass-symmetric 2-type Legendre surfaces in S5. Moreover, we show that pseudo-Hermitian mass-symmetric 2-type Legendre surfaces in S5 are the locally product of two pseudo-Hermitian circles.

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References

  1. C. Baikoussis and D. E. Blair, 2-type integral surfaces in S5(1), Tokyo J. Math. 14 (1991), no. 2, 345-356. https://doi.org/10.3836/tjm/1270130378
  2. D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics, 203, Birkhauser Boston, Inc., Boston, MA, 2002. https://doi.org/10.1007/978-1-4757-3604-5
  3. B.-Y. Chen, Total mean curvature and submanifolds of finite type, Series in Pure Mathematics, 1, World Scientific Publishing Co., Singapore, 1984. https://doi.org/10.1142/0065
  4. J. T. Cho, Geometry of contact strongly pseudo-convex CR-manifolds, J. Korean Math. Soc. 43 (2006), no. 5, 1019-1045. https://doi.org/10.4134/JKMS.2006.43.5.1019
  5. J.-E. Lee, Laplacians and Legendre surfaces in pseudo-Hermitian geometry, Bull. Iranian Math. Soc. 44 (2018), no. 4, 899-913. https://doi.org/10.1007/s41980-018-0058-1
  6. N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japan. J. Math. (N.S.) 2 (1976), no. 1, 131-190. https://doi.org/10.4099/math1924.2.131
  7. S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc. 314 (1989), no. 1, 349-379. https://doi.org/10.2307/2001446
  8. S. M. Webster, Pseudo-Hermitian structures on a real hypersurface, J. Differential Geom. 13 (1978), no. 1, 25-41. http://projecteuclid.org/euclid.jdg/1214434345 https://doi.org/10.4310/jdg/1214434345