RIEMANNIAN SUBMERSIONS OF SO0(2, 1)
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
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.
Abstract
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.
참고문헌 (6)
- Taechang Byun, "The topological matter of holonomy displacement on the principal U ( n ) -bundle over D n , m , related to complex surfaces", Journal of Geometry and Physics, 127, pp.112~127 (2018), Elsevier BV[DOI]
- Taechang Byun, "The topological aspect of the holonomy displacement on the principal U(n) bundles over Grassmannian manifolds", Topology and its Applications, 196, pp.8~21 (2015), Elsevier BV[DOI]
- T. Byun, "The geometry of SO(n)nㅣSO0(n; 1)", Geom. Dedicata, 161, pp.377~398 (2012)
- 최영기, "HOLONOMY DISPLACEMENTS IN THE HOPF BUNDLES OVER CHn AND THE COMPLEX HEISENBERG GROUPS", 대한수학회지, 49(4), pp.733~743 (2012), 대한수학회[DOI]
- D. Gromoll, "Metric foliations and curvature" (2009), Birkhauser Verlag
- U. Pinkall, "Hopf tori inS 3", Inventiones Mathematicae, 81(2), pp.379~386 (1985), Springer Science and Business Media LLC[DOI]