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.
雑誌名
Journal of mathematical sciences, the University of Tokyo
巻
4
号
3
ページ
649 - 662
発行年
1997
ISSN
13405705
書誌レコードID
AA11021653
フォーマット
application/pdf
日本十進分類法
415
Mathematical Reviews Number
MR1484606
Mathmatical Subject Classification
53C50(MSC1991)
53A30(MSC1991)
出版者
Graduate School of Mathematical Sciences, The University of Tokyo
Essential Conformal Fields in Pseudo-Riemannian Geometry. II
jms040308.pdf
(130.72KB)
