Inhomogeneous Einstein metrics on complex line bundles
- 1 March 1987
- journal article
- Published by IOP Publishing in Classical and Quantum Gravity
- Vol. 4 (2) , 213-225
- https://doi.org/10.1088/0264-9381/4/2/005
Abstract
Recent developments in higher-dimensional unified field theories have led to a great deal of interest in compact spaces admitting Einstein metrics. Almost all the physics literature on such spaces has been concerned with the very atypical case in which the space is homogeneous. The authors present a very simple construction of a wide class of inhomogeneous compact Einstein spaces with positive Ricci curvature found earlier by Berard-Bergery, (1982) which arise as certain 2-sphere bundles over an arbitrary Einstein-Kahler base space of positive Ricci curvature. Solutions on complete non-compact manifolds also exist, with negative or zero Ricci curvature.Keywords
This publication has 10 references indexed in Scilit:
- Einstein metrics on quaternionic line bundlesClassical and Quantum Gravity, 1986
- Gravitation, gauge theories and differential geometryPhysics Reports, 1980
- Métriques kählériennes et fibrés holomorphesAnnales Scientifiques de lʼÉcole Normale Supérieure, 1979
- A compact rotating gravitational instantonPhysics Letters B, 1978
- Taub-NUT instanton with an horizonPhysics Letters B, 1978
- Asymptotically flat self-dual solutions to euclidean gravityPhysics Letters B, 1978
- Calabi's conjecture and some new results in algebraic geometryProceedings of the National Academy of Sciences, 1977
- Gravitational instantonsPhysics Letters A, 1977
- Characterizations of complex projective spaces and hyperquadricsKyoto Journal of Mathematics, 1973
- Riemannian manifolds with positive mean curvatureDuke Mathematical Journal, 1941