Essential Conformal Fields in Pseudo-Riemannian Geometry. II

J. Math. Sci. Univ. Tokyo
Vol. 4 (1997), No. 3, Page 649--662.

Kühnel, W. ; Rademacher, H.-B.
Essential Conformal Fields in Pseudo-Riemannian Geometry. II
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We study conformal vector fields on pseudo- Riemannian manifolds. In the case of conformally flat manifolds, the main tool is the conformal development map into the projective quadric. On the other hand, we show that there exists a pseudo-Riemannian manifold carrying a complete and essential vector field which is not conformally flat. The example implies that there is no finite dimensional moduli space for such manifolds. Therefore, a pseudo-Riemannian analogue of Alekseevskii's theorem on the classification of essential conformal vector fields cannot be expected.

Keywords: conformal compactification, projective quadric, sphere inversion, conformal group, conformally closed, null cone at infinity

Mathematics Subject Classification (1991): 53C50, 53A30
Mathematical Reviews Number: MR1484606

Received: 1997-02-19