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J. F. Plebański, Some solutions of complex Einstein equations. J. Math. Phys. 16, 2395–2402 (1975).
J. D. Finley III and J. F. Plebadski, Further heavenly metrics and their symmetries. J. Math. Phys. 17, 585–596 (1976).
C. P. Boyer and J. F. Plebadski, Heavens and their integral manifolds. J. Math. Phys. 18, 1022–1031 (1977).
C. P. Boyer and J. F. Plebański, General relativity and G-structures. I. General theory and algebraically degenerate spaces. Rep. Math. Phys. 14, 111–145 (1978).
C. P. Boyer, J. D. Finley III, and J. F. Plebański, Complex general relativity, H and HH spaces —a survey of one approach. In General Relativity and Gravitation, Vol. 2, A. Held ed., Plenum Press, 1980, pp. 241–281.
R. Penrose, Nonlinear gravitons and curved twistar theory. GRG 7, 31–52 (l976).
R. Penrose and R. S. Ward, Twistars for flat and curved space-time. In General Relativity and Gravitation, Vol. 2, A. Held ed., Plenum Press, 1980, pp. 283–328.
R. O. Hansen, E. T. Newman, R. Penrose, and K. P. Tod, The metric and curvature properties of H-space. Oxford University preprint.
R. S. Ward, The self-dual Yang-Mills and Einstein equations. In Complex Manifold Techniques in Theoretical Physics, D. E. Lerner and P. D. Sommers eds., Pitman, 1979, pp. 12–34.
E. J. Flaherty, Hermitian and Kählerian Geometry in Relativity. Springer Verlag, 1976.
M. Ko, M. Ludvigsen, E. T. Newman, and K. P. Tod, The theory of H-space. Physics Reports 71, 51–139 (1981).
J. D. Finley III and J. F. Plebański, The classification of all H-spaces admitting a Killing vector. J. Math. Phys. 20, 1938–1945 (1979).
J. D. Finley III and J. F. Plebański, All algebraically degenerate H-spaces via HH-spaces. J. Math. Phys. 22, 667–674 (1981).
R. S. Ward, A class of self-dual solutions of Einstein's equations. Proc. R. Soc. London A363, 289–295 (1978).
K. P. Tod and R. S. Ward, Self-dual metrics with self-dual Killing vectors. Proc. R. Soc. London A358, 411–427 (1979).
W. D. Curtis, D. E. Lerner, and F. R. Miller, Complex pp waves and the nonlinear graviton construction. J. Math. Phys. 19, 2024–2027 (1978).
M. G. Eastwood, R. Penrose, and R. O. Wells, Cohomology and massless fields. Commun. Math. Phys. 78, 305–351 (1981).
C. P. Boyer and J. F. Plebański, An infinite hierarchy of conservation laws and nonlinear superposition principles for self-dual Einstein spaces. Preprint: Comunicaciones Técnicas IIMAS (1983).
R. S. Ward, On self-dual gauge fields. Phys. Lett. 61A, 81–82 (1977).
M. F. Atiyah and R. S. Ward, Instantons and algebraic geometry, Commun. Math. Phys. 55, 117–124 (1977).
M. F. Atiyah, N. J. Hitchin, and I. M. Singer, Self-duality in four-dimensional Riemannian geometry. Proc. R. Soc. London A362, 425–461 (1978).
E. Witten, An interpretation of classical Yang-Mills theory. Phys. Lett. 77B, 394–398 (1978).
J. Isenberg, P. B. Yasskin, and P. S. Green, Non-self-dual gauge fields. Phys. Lett. 78B, 462–464 (1978).
J. Isenberg and P. B. Yasskin, Twistor description of non-self-dual Yang-Mills fields. In Complex Manifold Techniques in Theoretical Physics, D. E. Lerner and P. D. Sommers eds., Pitman, 1979, pp. 180–206.
Yu. I. Manin, Flag superpsaces and supersymmetric Yang-Mills equations. preprint.
C. R. LeBrun, Spaces of complex geodesics and related structures. Oxford University thesis (1980).
C. R. LeBrun, The first formal neighbourhood of ambitwistor space for curved space-time. Preprint IHES/M/81/54.
Yu. I. Manin and I. B. Penkov, Null geodesics of complex Einstein spaces. J. Funct. Anal. Appl. 16, 64–66 (1982).
J. F. Plebański and I. Robinson, Left-degenerate vacuum metrics. Phys. Rev. Lett. 37, 493–495 (1976).
R. Penrose, Structure of space-time. In Batelle Rencontres 1967, C. M. de Witt and J. A. Wheeler, eds., Benjamin, 1968, pp. 121–235.
R. O. Wells, Complex manifolds and mathematical physics. Bull. Amer. Math. Soc. (new series) 1, 296–336 (1979).
K. Kodaira, On stability of complex submanifolds of complex manifolds. Amer. J. Math. 85, 79–94 (1963).
A. Weinstein, Lagrangian submanifolds and hamiltonian systems. Ann. Math. 98, 377–410 (1973).
A. Weinstein, Symplectic manifolds and their lagrangian submanifolds. Adv. Math. 6, 329–346 (1971).
V. Guillemin and S. Sternberg, Geometric Asymptotics. Mathematical Surveys 14, American Mathematical Society, 1977.
I. N. Bernshtein and B. I. Rozenfel'd, Homogeneous spaces of infinite-dimensional Lie algebras and characteristic classes of foliations. Russ. Math. Surv., 107–141 (19).
K. Yano and S. Ishihara, Tangent and Cotangent Bundles. Marcel Dekker, 1973.
R. O. Wells, Differential Analysis on Complex Manifolds. Springer Verlag, 1980.
R. S. Ward, Self-dual space-times with cosmological constant. Commun. Math. Phys. 78, 1–17 (1980).
E. T. Newman, J. R. Porter, and K. P. Tod, Twistor surfaces and right-flat spaces. GRG 9, 1129–1142 (1978).
S. Hawking, Gravitational instantons. Phys. Lett. 60A, 81–83 (1977).
M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, The inverse scattering transform-Fourier analysis for nonlinear problems. Studies in Applied Mathematics 53, 249–315 (1974).
I. M. Krichever and S. P. Novikov, Holomorphic bundles over algebraic curves and nonlinear equations. Russ. Math. Surv. 35, 53–79 (1980).
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Boyer, C.P. (1983). The geometry of complex self-dual Einstein spaces. In: Wolf, K.B. (eds) Nonlinear Phenomena. Lecture Notes in Physics, vol 189. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12730-5_2
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