Explicit self-dual metrics on ${\bf C}{\rm P}\sb 2\#\cdots\#{\bf C}{\rm P}\sb 2$

previous :: next

Explicit self-dual metrics on ${\bf C}{\rm P}\sb 2\#\cdots\#{\bf C}{\rm P}\sb 2$

Claude LeBrun

Source: J. Differential Geom. Volume 34, Number 1 (1991), 223-253.

Primary Subjects: 53C25

Secondary Subjects: 32L25, 35J05

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.jdg/1214446999
Mathematical Reviews number (MathSciNet): MR1114461
Zentralblatt MATH identifier: 0725.53067

back to Table of Contents

References

[1] M. Atiyah, N. Hitchin and I. Singer, Self-duality in four dimensional Riemannian geometry, Proc. Roy. Soc. London Ser. A 362 (1978) 425-461. It remains to be seen, of course, whether a self-dual 4-manifold with Moishezon twistor space is necessarily diffeomorphic to «CP2 .

Zentralblatt MATH: 0389.53011

Mathematical Reviews (MathSciNet): MR506229

[2] C. Boyer and J. Finley, Killing vectors in self-dual Euclidean Einstein spaces, J. Math. Phys. 23 (1982) 1126-1130.

Zentralblatt MATH: 0484.53051

Mathematical Reviews (MathSciNet): MR660020

[3] D. Bums, Twistors and harmonic maps, Lecture, Amer. Math. Soc. Conference, Charlotte, NC, October 1986.

[4] F. Campana, On twistor spaces of the class and , J. Differential Geometry 33 (1991) 541-549.

Zentralblatt MATH: 0694.32017

Mathematical Reviews (MathSciNet): MR1094468

[5] E. Cartan, Sur une classe d'espaces de Weyl, Ann. Sci. Ecole. Norm. Sup. 60 (1943) 1-16.

Zentralblatt MATH: 0028.30802

Mathematical Reviews (MathSciNet): MR14292

[6] A. Derdzinski, Self-dual Kahler manifolds and Einstein manifolds of dimension four, Compositio Math. 49 (1983) 405-433.

Zentralblatt MATH: 0527.53030

Mathematical Reviews (MathSciNet): MR707181

[7] S. K. Donaldson and R. Friedman, Connected sums of self-dual manifolds and deformations of singular spaces, Nonlinearity2 (1989) 197-239.

Zentralblatt MATH: 0671.53029

Mathematical Reviews (MathSciNet): MR994091

[8] A. Floer, Self-dual conformal structures on IC2 , J. Differential Geometry 33 (1991) 551-573.

Zentralblatt MATH: 0736.53046

Mathematical Reviews (MathSciNet): MR1094469

[9] R. Friedman, Simultaneous resolution of threefold double points, Math. Ann. 274 (1986) 671-689.

Zentralblatt MATH: 0576.14013

Mathematical Reviews (MathSciNet): MR848512

[10] G. W. Gibbons and S. W. Hawking, Gravitational multi-instantons, Phys. Lett. B78 (1978) 430-432.

[11] N. J. Hitchin, Polygons and gravitons, Math. Proc. Cambridge Philos. Soc. 83 (1979) 465-476.

Zentralblatt MATH: 0405.53016

Mathematical Reviews (MathSciNet): MR520463

[12] N. J. Hitchin, Polygons and gravitons, Kahlerian twistor spaces, Proc. London Math. Soc. 43 (1981) 133-150.

Zentralblatt MATH: 0474.14024

Mathematical Reviews (MathSciNet): MR623721

[13] N. J. Hitchin, Polygons and gravitons, Complex manifolds and Einstein's equations, Lecture Notes in Math., Vol. 970, Springer, Berlin, 1982, 73-99.

Zentralblatt MATH: 0405.53016

Mathematical Reviews (MathSciNet): MR699802

[14] N. J. Hitchin, Polygons and gravitons, Monopoles and geodesics, Comm. Math. Phys. 83 (1982) 579-602.

Zentralblatt MATH: 0502.58017

Mathematical Reviews (MathSciNet): MR649818

[15] P. E.Jones and K. P. Tod, Minitwistor spaces and Einstein-Weylspaces, Classical Quantum Gravity 2 (1985) 565-577.

Zentralblatt MATH: 0575.53042

Mathematical Reviews (MathSciNet): MR795102

[16] C. LeBrun, Twistor CR manifolds and three-dimensional conformal geometry, Trans. Amer. Math. Soc. 284 (1984) 601-616.

Zentralblatt MATH: 0513.53006

Mathematical Reviews (MathSciNet): MR743735

[17] C. LeBrun, Foliated CR manifolds, J. Differential Geometry 22 (1985) 81-96.

Zentralblatt MATH: 0563.32011

Mathematical Reviews (MathSciNet): MR826425

[18] C. LeBrun, On the topology of self dual manifolds, Proc. Amer. Math. Soc.98 (1986) 637-640.

Zentralblatt MATH: 0606.53029

Mathematical Reviews (MathSciNet): MR861766

[19] C. LeBrun, Poon's self-dual metrics and Kahler geometry, J. Differential Geometry 28 (1988) 341-343.

Zentralblatt MATH: 0651.53047

Mathematical Reviews (MathSciNet): MR961518

[20] C. LeBrun, Counter-examples to the generalizedpositiveaction conjecture, Comm. Math. Phys. 118 (1988) 591-596.

Zentralblatt MATH: 0659.53050

Mathematical Reviews (MathSciNet): MR962489

[21] Q. H. Park, Extended conformal symmetries in real heavens, Preprint90-037, University of Maryland, 1989.

Mathematical Reviews (MathSciNet): MR1041737

[22] H. Pedersen, Einstein metrics, spinning-top motions, and monopoles, Math. Ann. 274 (1986) 35-59.

Zentralblatt MATH: 0566.53058

Mathematical Reviews (MathSciNet): MR834105

[23] H. Pedersen and K. P. Tod, Three dimensional Einstein-Weyl geometry, Preprint, Odense Universitet, 1988; Advances in Math., to appear.

Zentralblatt MATH: 0778.53041

Mathematical Reviews (MathSciNet): MR1171902

[24] M. Pontecorvo, On twistor spaces of anti-self-dual Hermitian surfaces, Trans. Amer. Math. Soc, to appear.

Zentralblatt MATH: 0754.53053

Mathematical Reviews (MathSciNet): MR1050087

[25] Y. S. Poon, Compact self-dual manifolds with positive scalar curvature, J. Differential Geometry 24 (1986) 97-132.

Zentralblatt MATH: 0583.53054

Mathematical Reviews (MathSciNet): MR857378

[26] Y. S. Poon, Algebraic dimension of twistor spaces, Math. Ann. 282 (1988) 621-627.

Zentralblatt MATH: 0665.32014

Mathematical Reviews (MathSciNet): MR970223

[27] R. S. Ward, Einstein-Weyl spaces and SUfoo Toda fields, Classical Quantum Gravity 7 (1990) L95-L98.

Zentralblatt MATH: 0687.53044

Mathematical Reviews (MathSciNet): MR1045295

previous :: next

Journal of Differential Geometry

Credits