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Bull. Korean Math. Soc. 2012; 49(5): 1101-1129

Printed September 30, 2012

https://doi.org/10.4134/BKMS.2012.49.5.1101

Copyright © The Korean Mathematical Society.

Homogeneous submersions of 3-dimensional geometries

Kyung Bai Lee and Joonsang Park

University of Oklahoma, Dongguk University

Abstract

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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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