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A note on the circle actions on Einstein manifolds

Published online by Cambridge University Press:  17 April 2009

Seungsu Hwang
Seungsu Hwang
Affiliation:
Hankuk Aviation University, 200–1 Hwajong-dong, Koyang, Kyonggi-do, Korea 412–791, e-mail: seungsu@mail.hangkong.ac.kr
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Abstract

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A fundamental result in the theory of black holes due to Hawking asserts that the event horizon of a black hole in the stationary space-time is a 2-sphere topologically. In this article we prove the Riemannian analogue of Hawking's result. In other words, we prove that each bolt of a 4-dimensional complete noncompact Einstein manifold of zero scalar curvature admitting a semifree isometric circle action is a 2-sphere topologically. We also study the structure of the orbit space of an Einstein manifold admitting a free isometric circle action.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 1 , February 2001 , pp. 83 - 91
Copyright
Copyright © Australian Mathematical Society 2001

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