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From Geometry to Quantum Mechanics pp 69–83Cite as

Global Structures of Compact Conformally Flat Semi-Symmetric Spaces of Dimension 3 and of Non-Constant Curvature

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Part of the book series: Progress in Mathematics ((PM,volume 252))

Abstract

Let (M, g) be a compact connected locally conformally flat semi-symmetric space of dimension 3 and with principal Ricci curvatures ρ 1 = ρ 2 ≠ ρ 3 = 0. Then M is a Seifert fibre space. Moreover, in case the holonomy group is discrete, M is commensurable to a Kleinian manifold. If the holonomy group is indiscrete, (M, ḡ) is a hyperbolic surface bundle over a circle and (M, g) has negative scalar curvature. Here ḡ denotes a metric induced from the flat conformal structure.

The author is partially supported by the Grant-in-Aid for Scientific Researches ((C)(2), No. 16540089) Japan Society for the Promotion of Science.

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Author information

Authors and Affiliations

  1. Faculty of Information Engineering, Fukuoka Institute of Technology, Higashi-ku, Fukuoka, 811-0295, Japan

    Midori S. Goto

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  1. Midori S. Goto
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Faculty of Science and Technology, Keio University, Hiyoshi, Yokohama, 223-8522, Japan

    Yoshiaki Maeda

  2. Department of Natural Science, Nippon Sports Science University, 7-1-1, Fukazawa, Setagaya-ku, Tokyo, 158-8508, Japan

    Takushiro Ochiai

  3. Facultät für Mathematik, Universität Wein, Nordbergstrasse 15, A-1090, Wein, Austria

    Peter Michor

  4. Department of Mathematics, Tokyo University of Science, Kagurazaka, Tokyo, 102-8601, Japan

    Akira Yoshioka

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© 2007 Birkhäuser Boston

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Goto, M.S. (2007). Global Structures of Compact Conformally Flat Semi-Symmetric Spaces of Dimension 3 and of Non-Constant Curvature. In: Maeda, Y., Ochiai, T., Michor, P., Yoshioka, A. (eds) From Geometry to Quantum Mechanics. Progress in Mathematics, vol 252. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4530-4_5

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