대한수학회지 (Journal of the Korean Mathematical Society)

  • 제58권6호
  • /
  • Pages.1407-1419
  • /
  • 2021
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

RIEMANNIAN SUBMERSIONS OF SO0(2, 1)

  • Byun, Taechang (Department of Mathematics and Statistics Sejong University)
  • 투고 : 2021.01.08
  • 심사 : 2021.02.09
  • 발행 : 2021.11.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

The Iwasawa decomposition NAK of the Lie group G = SO0(2, 1) with a left invariant metric produces Riemannian submersions G → N\G, G → A\G, G → K\G, and G → NA\G. For each of these, we calculate the curvature of the base space and the lifting of a simple closed curve to the total space G. Especially in the first case, the base space has a constant curvature 0; the holonomy displacement along a (null-homotopic) simple closed curve in the base space is determined only by the Euclidean area of the region surrounded by the curve.

키워드

과제정보

The author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(2018R1D1A1A02047995).

참고문헌

  1. T. Byun, The topological matter of holonomy displacement on the principal U(n)-bundle over Dn,m, related to complex surfaces, J. Geom. Phys. 127 (2018), 112-127. https://doi.org/10.1016/j.geomphys.2018.02.004
  2. T. Byun and Y. Choi, The topological aspect of the holonomy displacement on the principal U(n) bundles over Grassmannian manifolds, Topology Appl. 196 (2015), part A, 8-21. https://doi.org/10.1016/j.topol.2015.09.007
  3. T. Byun, K. Jo, and K. B. Lee, The geometry of SO(n)\SO0(n, 1), Geom. Dedicata 161 (2012), 377-398. https://doi.org/10.1007/s10711-012-9710-8
  4. Y. Choi and K. B. Lee, Holonomy displacements in the Hopf bundles over ℂHn and the complex Heisenberg groups, J. Korean Math. Soc. 49 (2012), no. 4, 733-743. https://doi.org/10.4134/JKMS.2012.49.4.733
  5. D. Gromoll and G. Walschap, Metric foliations and curvature, Progress in Mathematics, 268, Birkhauser Verlag, Basel, 2009. https://doi.org/10.1007/978-3-7643-8715-0
  6. U. Pinkall, Hopf tori in S3, Invent. Math. 81 (1985), no. 2, 379-386. https://doi.org/10.1007/BF01389060