Abstract
We give here a geometric proof of the existence of certain local coordinates on a pseudo-Riemannian manifold admitting a closed conformal vector field.
Open Access
Closed conformal vector fields on pseudo-Riemannian manifolds
Received01 Mar 2006
Revised24 Jul 2006
Accepted08 Aug 2006
Published12 Oct 2006
References
D. Alekseevski, “Self-similar Lorentzian manifolds,” Annals of Global Analysis and Geometry, vol. 3, no. 1, pp. 59–84, 1985.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetH. W. Brinkmann, “Einstein spaces which are mapped conformally on each other,” Mathematische Annalen, vol. 94, no. 1, pp. 119–145, 1925.
View at: Publisher Site | Google Scholar | MathSciNetA. Fialkow, “Conformal geodesics,” Transactions of the American Mathematical Society, vol. 45, no. 3, pp. 443–473, 1939.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetY. Kerbrat, “Transformations conformes des variétés pseudo-riemanniennes,” Journal of Differential Geometry, vol. 11, no. 4, pp. 547–571, 1976.
View at: Google Scholar | Zentralblatt MATH | MathSciNetW. Kühnel and H.-B. Rademacher, “Essential conformal fields in pseudo-Riemannian geometry,” Journal de Mathématiques Pures et Appliquées. Neuvième Série, vol. 74, no. 5, pp. 453–481, 1995.
View at: Google Scholar | Zentralblatt MATH | MathSciNetY. Tashiro, “Complete Riemannian manifolds and some vector fields,” Transactions of the American Mathematical Society, vol. 117, pp. 251–275, 1965.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetK. Yano, “Concircular geometry III. Theory of curves,” Proceedings of the Imperial Academy of Tokyo, vol. 16, pp. 442–448, 1940.
View at: Google Scholar | Zentralblatt MATH | MathSciNetK. Yano, “Concircular geometry IV. Theory of subspaces,” Proceedings of the Imperial Academy of Tokyo, vol. 16, pp. 505–511, 1940.
View at: Google Scholar | Zentralblatt MATH | MathSciNetK. Yano, “Concircular geometry. I. Concircular transformations,” Proceedings of the Imperial Academy of Tokyo, vol. 16, pp. 195–200, 1940.
View at: Google Scholar | Zentralblatt MATH | MathSciNetK. Yano, “Concircular geometry. II. Integrability conditions of ,” Proceedings of the Imperial Academy of Tokyo, vol. 16, pp. 354–360, 1940.
View at: Google Scholar | Zentralblatt MATH | MathSciNetK. Yano, “Concircular geometry. V. Einstein spaces,” Proceedings of the Imperial Academy of Tokyo, vol. 18, pp. 446–451, 1942.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
Copyright
Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.