Homogeneous submersions of 3-dimensional geometries
Bull. Korean Math. Soc. 2012 Vol. 49, No. 5, 1101-1129
Printed September 30, 2012
Kyung Bai Lee and Joonsang Park
University of Oklahoma, Dongguk University
Abstract : We study the geometry of the images of 1-dimensional homogeneous submersions for each of the model spaces $X$ of the eight 3-dimensional geometries. In particular, We shall calculate the group of isometries and the curvatures of the base surfaces for each of the model spaces of 3-dimensional geometries, with respect to every closed subgroup of the isometries of $X$ acting freely.
Keywords : homogeneous, submersion, orbit space, foliation, 8-geometry, Gaussian curvature
MSC numbers : 53C30, 53C12
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