Duke Mathematical Journal
- Duke Math. J.
- Volume 63, Number 3 (1991), 723-743.
On complete quaternionic-Kähler manifolds
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Article information
Source
Duke Math. J., Volume 63, Number 3 (1991), 723-743.
Dates
First available in Project Euclid: 20 February 2004
Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077296077
Digital Object Identifier
doi:10.1215/S0012-7094-91-06331-3
Mathematical Reviews number (MathSciNet)
MR1121153
Zentralblatt MATH identifier
0764.53045
Subjects
Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 32L25: Twistor theory, double fibrations [See also 53C28] 58D27: Moduli problems for differential geometric structures
Citation
LeBrun, Claude. On complete quaternionic-Kähler manifolds. Duke Math. J. 63 (1991), no. 3, 723--743. doi:10.1215/S0012-7094-91-06331-3. https://projecteuclid.org/euclid.dmj/1077296077
References
- [1] M. F. Atiyah, N. J. Hitchin, and I. M. Singer, Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London Ser. A 362 (1978), no. 1711, 425–461.Mathematical Reviews (MathSciNet): MR80d:53023
Zentralblatt MATH: 0389.53011
Digital Object Identifier: doi:10.1098/rspa.1978.0143 - [2] T. N. Bailey and M. G. Eastwood, Complex paraconformal manifolds—their differential geometry and twistor theory, Forum Math. 3 (1991), no. 1, 61–103.Mathematical Reviews (MathSciNet): MR92a:32038
Zentralblatt MATH: 0728.53005
Digital Object Identifier: doi:10.1515/form.1991.3.61 - [3] L. Berard-Bergery, Une généralisation de la théorie des twisteurs de Penrose, unpublished lectures at the Universite de Nancy I, 1983.
- [4] M. Berger, Remarques sur les groupes d'holonomie des variétés Riemanniennes, C. R. Acad. Sci. Paris Sér. A-B 262 (1966), 1316–1318.
- [5] A. L. Besse, Einstein Manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 10, Springer, Berlin, 1987.
- [6] R. L. Bryant, Metrics with exceptional holonomy, Ann. of Math. (2) 126 (1987), no. 3, 525–576.Mathematical Reviews (MathSciNet): MR89b:53084
Zentralblatt MATH: 0637.53042
Digital Object Identifier: doi:10.2307/1971360
JSTOR: links.jstor.org - [7] A. Douady, Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné, Ann. Inst. Fourier (Grenoble) 16 (1966), no. fasc. 1, 1–95.
- [8] M. G. Eastwood and C. R. LeBrun, Fattening complex manifolds, curvature, and Kodaira-Spencer maps, preprint.Mathematical Reviews (MathSciNet): MR1165875
Zentralblatt MATH: 0748.32017
Digital Object Identifier: doi:10.1016/0393-0440(92)90045-3 - [9] M. G. Eastwood, R. Penrose, and R. O. Wells Jr., Cohomology and massless fields, Comm. Math. Phys. 78 (1981), no. 3, 305–351.Mathematical Reviews (MathSciNet): MR83d:81052
Zentralblatt MATH: 0465.58031
Digital Object Identifier: doi:10.1007/BF01942327
Project Euclid: euclid.cmp/1103908690 - [10] P. A. Griffiths, The extension problem in complex analysis. II. embeddings with positive normal bundle, Amer. J. Math. 88 (1966), 366–446.Mathematical Reviews (MathSciNet): MR34:6796
Zentralblatt MATH: 0147.07502
Digital Object Identifier: doi:10.2307/2373200
JSTOR: links.jstor.org - [11] C. R. Graham and J. Lee, Einstein metrics on the ball with prescribed conformal infinity, preprint.
- [12] K. Kodaira, On stability of compact submanifolds of complex manifolds, Amer. J. Math. 85 (1963), 79–94.Mathematical Reviews (MathSciNet): MR27:3002
Zentralblatt MATH: 0173.33101
Digital Object Identifier: doi:10.2307/2373187
JSTOR: links.jstor.org - [13] K. Kodaira and D. C. Spencer, On deformations of complex analytic structures. I& II, Ann. of Math. (2) 67 (1958), 328–466.Mathematical Reviews (MathSciNet): MR22:3009
Zentralblatt MATH: 0128.16901
Digital Object Identifier: doi:10.2307/1970009
JSTOR: links.jstor.org - [14] C. R. LeBrun, $\cal H$-space with a cosmological constant, Proc. Roy. Soc. London Ser. A 380 (1982), no. 1778, 171–185.Mathematical Reviews (MathSciNet): MR83d:83019
Zentralblatt MATH: 0549.53042
Digital Object Identifier: doi:10.1098/rspa.1982.0035
JSTOR: links.jstor.org - [15] C. LeBrun, A rigidity theorem for quaternionic-Kähler manifolds, Proc. Amer. Math. Soc. 103 (1988), no. 4, 1205–1208.Mathematical Reviews (MathSciNet): MR89h:53105
Zentralblatt MATH: 0655.53056
Digital Object Identifier: doi:10.2307/2047113
JSTOR: links.jstor.org - [16] C. LeBrun, Quaternionic-Kähler manifolds and conformal geometry, Math. Ann. 284 (1989), no. 3, 353–376.Mathematical Reviews (MathSciNet): MR90e:53062
Zentralblatt MATH: 0674.53036
Digital Object Identifier: doi:10.1007/BF01442490 - [17] H. Pedersen, Einstein metrics, spinning top motions and monopoles, Math. Ann. 274 (1986), no. 1, 35–59.Mathematical Reviews (MathSciNet): MR87i:53070
Zentralblatt MATH: 0566.53058
Digital Object Identifier: doi:10.1007/BF01458016 - [18] H. Pedersen and Y. S. Poon, Twistorial construction of quaternionic manifolds, Proceedings of the Sixth International Colloquium on Differential Geometry (Santiago de Compostela, 1988), Cursos Congr. Univ. Santiago de Compostela, vol. 61, Univ. Santiago de Compostela, Santiago de Compostela, 1989, pp. 207–218.
- [19] R. Penrose, Nonlinear gravitons and curved twistor theory, General Relativity and Gravitation 7 (1976), no. 1, 31–52.Mathematical Reviews (MathSciNet): MR55:11905
Zentralblatt MATH: 0354.53025
Digital Object Identifier: doi:10.1007/BF00762011 - [20] R. Penrose and W. Rindler, Spinors and space-time. Vol. 2, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1986.
- [21] Y.-S. Poon and S. M. Salamon, Quaternionic Kähler $8$-manifolds with positive scalar curvature, J. Differential Geom. 33 (1991), no. 2, 363–378.Mathematical Reviews (MathSciNet): MR92b:53071
Zentralblatt MATH: 0733.53035
Project Euclid: euclid.jdg/1214446322 - [22] M. Namba, On maximal families of compact complex submanifolds of complex manifolds, Tohoku Math. J. (2) 24 (1972), 581–609.Mathematical Reviews (MathSciNet): MR48:6471
Zentralblatt MATH: 0254.32023
Digital Object Identifier: doi:10.2748/tmj/1178241448
Project Euclid: euclid.tmj/1178241448 - [23] S. Salamon, Riemannian geometry and holonomy groups, Pitman Research Notes in Mathematics Series, vol. 201, Longman Scientific & Technical, Harlow, 1989.
- [24] S. Salamon, Quaternionic Kähler manifolds, Invent. Math. 67 (1982), no. 1, 143–171.Mathematical Reviews (MathSciNet): MR83k:53054
Zentralblatt MATH: 0486.53048
Digital Object Identifier: doi:10.1007/BF01393378 - [25] M. Thornber, Vanishing theorems for quaternionic-Kähler manifolds, Ph.D. thesis, State Univ. of New York, Stony Brook, 1989.
- [26] R. S. Ward, Self-dual space-times with cosmological constant, Comm. Math. Phys. 78 (1980/81), no. 1, 1–17.Mathematical Reviews (MathSciNet): MR82g:83004
Zentralblatt MATH: 0468.53019
Digital Object Identifier: doi:10.1007/BF01941967
Project Euclid: euclid.cmp/1103908499

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