previous :: next
Compact Einstein-Weyl manifolds with large symmetry group
Anders Bisbjerg Madsen, Henrik Pedersen, Yat Sun Poon, and Andrew Swann
Source: Duke Math. J. Volume 88, Number 3
(1997), 407-434.
First Page:
Show
Hide
Related Works:
Primary Subjects:
53C25
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077241763
Mathematical Reviews number (MathSciNet): MR1455527
Zentralblatt MATH identifier: 0881.53041
Digital Object Identifier: doi:10.1215/S0012-7094-97-08817-7
References
[1] L. Bérard-Bergery, Sur la courbure des métriques riemanniennes invariantes des groupes de Lie et des espaces homogènes, Ann. Sci. École Norm. Sup. (4) 11 (1978), no. 4, 543–576.
Mathematical Reviews (MathSciNet): MR80k:53078
Zentralblatt MATH: 0426.53038
[2] L. Bérard-Bergery, Sur de nouvelles variétés riemanniennes d'Einstein, Institut Élie Cartan, 6, Inst. Élie Cartan, vol. 6, Univ. Nancy, Nancy, 1982, pp. 1–60.
Mathematical Reviews (MathSciNet): MR85b:53048
Zentralblatt MATH: 0544.53038
[3] A. L. Besse, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 10, Springer-Verlag, Berlin, 1987.
Mathematical Reviews (MathSciNet): MR88f:53087
Zentralblatt MATH: 0613.53001
[4] E. Cartan, Sur une classe d'espaces de Weyl, Ann. Sci. École Norm. Sup. (3) 60 (1943), 1–16.
Mathematical Reviews (MathSciNet): MR7,265e
Zentralblatt MATH: 0028.30802
[5] S. K. Donaldson and P. B. Kronheimer, The geometry of four-manifolds, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1990.
Mathematical Reviews (MathSciNet): MR92a:57036
Zentralblatt MATH: 0820.57002
[6] P. Gauduchon, La $1$-forme de torsion d'une variété hermitienne compacte, Math. Ann. 267 (1984), no. 4, 495–518.
Mathematical Reviews (MathSciNet): MR87a:53101
Zentralblatt MATH: 0523.53059
Digital Object Identifier: doi:10.1007/BF01455968
[7] P. Gauduchon, Structures de Weyl-Einstein, espaces de twisteurs et variétés de type $S\sp 1\times S\sp 3$, J. Reine Angew. Math. 469 (1995), 1–50.
Mathematical Reviews (MathSciNet): MR97d:53048
Zentralblatt MATH: 0858.53039
Digital Object Identifier: doi:10.1515/crll.1995.469.1
[8] N. J. Hitchin, Complex manifolds and Einstein's equations, Twistor geometry and nonlinear systems (Primorsko, 1980), Lecture Notes in Math., vol. 970, Springer, Berlin, 1982, pp. 73–99.
Mathematical Reviews (MathSciNet): MR84i:32041
Zentralblatt MATH: 0507.53025
Digital Object Identifier: doi:10.1007/BFb0066025
[9] G. R. Jensen, Homogeneous Einstein spaces of dimension four, J. Differential Geometry 3 (1969), 309–349.
Mathematical Reviews (MathSciNet): MR41:6100
Zentralblatt MATH: 0194.53203
Project Euclid: euclid.jdg/1214429056
[10] P. E. Jones and K. P. Tod, Minitwistor spaces and Einstein-Weyl spaces, Classical Quantum Gravity 2 (1985), no. 4, 565–577.
Mathematical Reviews (MathSciNet): MR87b:53115
Zentralblatt MATH: 0575.53042
Digital Object Identifier: doi:10.1088/0264-9381/2/4/021
[11] J. Lafontaine, The theorem of Lelong-Ferrand and Obata, Conformal geometry (Bonn, 1985/1986), Aspects Math., E12, Vieweg, Braunschweig, 1988, pp. 93–103.
Mathematical Reviews (MathSciNet): MR90c:53036
Zentralblatt MATH: 0668.53022
[12] C. R. LeBrun, Self-dual manifolds and hyperbolic geometry, Einstein metrics and Yang-Mills connections (Sanda, 1990), Lecture Notes in Pure and Appl. Math., vol. 145, Dekker, New York, 1993, pp. 99–131.
Mathematical Reviews (MathSciNet): MR94h:53060
Zentralblatt MATH: 0802.53010
[13] J. Lelong-Ferrand, Transformations conformes et quasi-conformes des variétés riemanniennes compactes (démonstration de la conjecture de A. Lichnerowicz), Acad. Roy. Belg. Cl. Sci. Mém. Coll. in–8$\deg\$(2) 39 (1971), no. 5, 44, Acad. Roy. Belgique, Brussels.
Mathematical Reviews (MathSciNet): MR48:1100
Zentralblatt MATH: 0215.50902
[14] A. B. Madsen, Bianchi IX Kähler metrics are also Einstein-Weyl, preprint.
Mathematical Reviews (MathSciNet): MR1477813
Zentralblatt MATH: 0899.53040
Digital Object Identifier: doi:10.1088/0264-9381/14/9/018
[15] A. B. Madsen, Higher-dimensional cohomogeneity-one Einstein-Weyl solutions, in preparation.
[16] A. B. Madsen, Compact Einstein-Weyl manifolds with large symmetry group, Ph.D. thesis, Odense Univ., 1995.
[17]1 P. S. Mostert, On a compact Lie group acting on a manifold, Ann. of Math. (2) 65 (1957), 447–455.
Mathematical Reviews (MathSciNet): MR19,44b
Zentralblatt MATH: 0080.16702
Digital Object Identifier: doi:10.2307/1970056
JSTOR: links.jstor.org
[17]2 P. S. Mostert, Errata, “On a compact Lie group acting on a manifold”, Ann. of Math. (2) 66 (1957), 589.
Mathematical Reviews (MathSciNet): MR20:2395
Zentralblatt MATH: 0080.16702
Digital Object Identifier: doi:10.2307/1969911
[18] M. Obata, The conjectures on conformal transformations of Riemannian manifolds, J. Differential Geometry 6 (1971/72), 247–258.
Mathematical Reviews (MathSciNet): MR46:2601
Zentralblatt MATH: 0236.53042
Project Euclid: euclid.jdg/1214430407
[19] B. O'Neill, Semi-Riemannian geometry, Pure and Applied Mathematics, vol. 103, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1983.
Mathematical Reviews (MathSciNet): MR85f:53002
Zentralblatt MATH: 0531.53051
[20] J. Parker, $4$-dimensional $G$-manifolds with $3$-dimensional orbits, Pacific J. Math. 125 (1986), no. 1, 187–204.
Mathematical Reviews (MathSciNet): MR88e:57033
Zentralblatt MATH: 0599.57016
Project Euclid: euclid.pjm/1102700219
[21] H. Pedersen, Y. S. Poon, and A. F. Swann, The Hitchin-Thorpe inequality for Einstein- Weyl manifolds, Bull. London Math. Soc. 26 (1994), no. 2, 191–194.
Mathematical Reviews (MathSciNet): MR95h:53067
Zentralblatt MATH: 0810.53037
Digital Object Identifier: doi:10.1112/blms/26.2.191
[22] H. Pedersen, Y. S. Poon, and A. F. Swann, Einstein-Weyl deformations and submanifolds, Internat. J. Math. 7 (1996), no. 5, 705–719.
Mathematical Reviews (MathSciNet): MR97g:53057
Zentralblatt MATH: 0867.53042
Digital Object Identifier: doi:10.1142/S0129167X96000372
[23] H. Pedersen and A. F. Swann, Einstein-Weyl geometry, the Bach tensor and conformal scalar curvature, J. Reine Angew. Math. 441 (1993), 99–113.
Mathematical Reviews (MathSciNet): MR94k:53063
Zentralblatt MATH: 0776.53027
Digital Object Identifier: doi:10.1515/crll.1993.440.99
[24] H. Pedersen and K. P. Tod, Three-dimensional Einstein-Weyl geometry, Adv. Math. 97 (1993), no. 1, 74–109.
Mathematical Reviews (MathSciNet): MR93m:53042
Zentralblatt MATH: 0778.53041
Digital Object Identifier: doi:10.1006/aima.1993.1002
[25] K. P. Tod, Compact $3$-dimensional Einstein-Weyl structures, J. London Math. Soc. (2) 45 (1992), no. 2, 341–351.
Mathematical Reviews (MathSciNet): MR93d:53058
Zentralblatt MATH: 0761.53026
Digital Object Identifier: doi:10.1112/jlms/s2-45.2.341
[26] R. S. Ward, Einstein-Weyl spaces and $\rm SU(\infty)$ Toda fields, Classical Quantum Gravity 7 (1990), no. 4, L95–L98.
Mathematical Reviews (MathSciNet): MR91g:83019
Zentralblatt MATH: 0687.53044
[27] H. Weyl, Raum, Zeit, Materie: Vorlesungen über allgemeine Relativitätstheorie, 5th ed., Springer-Verlag, Berlin, 1923.
[28] J. A. Wolf, Spaces of Constant Curvature, McGraw-Hill Book Co., New York, 1967.
Mathematical Reviews (MathSciNet): MR36:829
Zentralblatt MATH: 0162.53304
previous :: next
Duke Mathematical Journal
