COMPLEX GENERAL RELATIVITY
1 INTRODUCTION TO COMPLEX SPACE-TIME 1 1 FROM LORENTZIAN SPACE-TIME TO COMPLEX SPACE-TIME 1 2 COMPLEX MANIFOLDS 1 3 AN OUTLINE OF THIS WORK 2 TWO-COMPONENT SPINOR CALCULUS 2 1 TWO-COMPONENT SPINOR CALCULUS 2 2 CURVATURE IN GENERAL RELATIVITY 2 3 PETROV CLASSIFICATION 3 CONFORMAL GRAVITY 3 1 C-SPACES 3 2 EINSTEIN SPACES 3 3 COMPLEX SPACE-TIMES 3 4 COMPLEX EINSTEIN SPACES 3 5 CONFORMAL INFINITY 4 TWISTOR SPACES 4 1 ?-PLANES IN MINKOWSKI SPACE-TIME 4 2 ?-SURFACES AND TWISTOR GEOMETRY 4 3 GEOMETRICAL THEORY OF PARTIAL DIFFERENTIAL EQUATIONS 5 PENROSE TRANSFORM FOR GRAVITATION 5 1 ANTI-SELF-DUAL SPACE-TIMES 5 2 BEYOND ANTI-SELF-DUALITY 6 2 FROBENIUS’ THEOREM FOR THEORIES WITH TORSION 8 6 3 SPINOR RICCI IDENTITIES FOR COMPLEX U4 THEORY 8 6 4 INTEGRABILITY CONDITION FOR ? -SURFACES 6 5 CONCLUDING REMARKS 9 7 S P I N- FIELDS IN RIEMANNIAN GEOMETRIES 9 7 1 DIRAC AND WEYL EQUATIONS IN TWO-COMPONENT SPINOR FORM 7 3 SELF-ADJOINTNESS OF THE BOUNDARY-VALUE PROBLEM 7 4 GLOBAL THEORY OF THE DIRAC OPERATOR 8 SPIN- POTENTIALS 8 1 INTRODUCTION 8 2 SPIN-LOWERING OPERATORS IN COSMOLOGY 8 4 DIRAC’S SPIN- POTENTIALS IN COSMOLOGY 8 5 BOUNDARY CONDITIONS IN SUPERGRAVITY 8 7 COMPATIBILITY CONDITIONS 8 8 ADMISSIBLE BACKGROUND FOUR-GEOMETRIES 8 10 RESULTS AND OPEN PROBLEMS 9 1 INTRODUCTION 2 – 9 10 QUANTIZATION OF FIELD THEORIES