Access the full text.
Sign up today, get DeepDyve free for 14 days.
T. Bailey, M. Eastwood (1990)
Conformal circles and parametrizations of curves in conformal manifolds, 108
D. Burns (1986)
Some Examples of the Twistor Construction
M. Eastwood, J. Rice (1987)
Conformally invariant differential operators on Minkowski space and their curved analoguesCommunications in Mathematical Physics, 109
M. Atiyah, N. Hitchin, I. Singer (1978)
Self-duality in four-dimensional Riemannian geometryProceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 362
N. Hitchin (1980)
Linear field equations on self-dual spacesProceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 370
M. Eastwood, R. Penrose, R. Wells (1981)
Cohomology and massless fieldsCommunications in Mathematical Physics, 78
(1923)
Les espaces conexion conforme
(1955)
The theory of the Lie derivative and its applications
H. Whitney, F. Bruhat (1959)
Quelques propriétés fondamentales des ensembles analytiques-réelsCommentarii Mathematici Helvetici, 33
(1990)
Invariant operators. Twistors in mathematics and physics (Eds
C. LeBrun (1983)
Spaces of complex null geodesics in complex-Riemannian geometryTransactions of the American Mathematical Society, 278
R. Baston, M. Eastwood (1990)
The Penrose Transform: Its Interaction with Representation Theory
C. Brun (1986)
Thickenings and gauge fieldsClassical and Quantum Gravity, 3
S. Salamon (1986)
Differential geometry of quaternionic manifoldsAnnales Scientifiques De L Ecole Normale Superieure, 19
M. Eastwood (1985)
The generalized Penrose-Ward transformMathematical Proceedings of the Cambridge Philosophical Society, 97
M. Eastwood (1984)
Complexification, twistor theory and harmonic maps from Riemann surfacesBulletin of the American Mathematical Society, 11
C. Boyer (1988)
A note on hyperhermitian four-manifolds, 102
R. Ward (1980)
Self-dual space-times with cosmological constantCommunications in Mathematical Physics, 78
M. Eastwood (1988)
THE PENROSE TRANSFORM FOR CURVED AMBITWISTOR SPACEQuarterly Journal of Mathematics, 39
S. Gindikin (1982)
Integral geometry and twistors, 970
J. Humphreys (1973)
Introduction to Lie Algebras and Representation Theory
Rod Gover (1989)
CONFORMALLY INVARIANT OPERATORS OF STANDARD TYPEQuarterly Journal of Mathematics, 40
R. Baston (1985)
The algebraic construction of invariant differential operators
(1975)
Differential operators on principal aifme spaces and investigation of g-modules. Lie groups and their representations (Ed. I.M
S. Salamon (1982)
Quaternionic Kähler manifoldsInventiones mathematicae, 67
C. LeBrun (1985)
Ambi-twistors and Einstein's equationsClassical and Quantum Gravity, 2
K. Kodalra (1962)
A Theorem Of Completeness Of Characteristic Systems For Analytic Families Of Compact Submanifolds Of Complex ManifoldsAnnals of Mathematics, 75
R. Penrose (1976)
Nonlinear gravitons and curved twistor theoryGeneral Relativity and Gravitation, 7
Abstract. A complex paraconformal manifold is a/^-dimensional complex manifold (/?, q > 2) whose tangent bündle factors äs a tensor product of two bundles of ranks p and q. We also assume that we are given a fixed isomorphism of the highest exterior powers of the two bundles. Examples of such manifolds include 4-dimensional conformal manifolds (with spin structure) and complexified quaternionic, quaternionic Kahler and hyperKähler manifolds. We develop the differential geomety of these structures, which is formally very similar to that of the special case of four dimensional conformal structures [30]. The examples have the property that they have a rieh twistor theory, which we discuss in a unified way in the paraconformal category. In particular, we consider the 'non-linear graviton' construction [29], and discuss the structure on the twistor space corresponding to quaternionic Kahler and hyperKähler metrics. We also define a family of special curves for these structures which in the 4-dimensional conformal case coincide with the conformal circles [34,2]. These curves have an intrinsic, naturally defined projective structure. In the particular case of complexified 4Ä>dimensional quaternionic structures, we obtain a distinguished 8fc + l parameter family of special curves saüsfying a third order ODE in
Forum Mathematicum – de Gruyter
Published: Jan 1, 1991
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.