Front Cover; Huygens' Principle and Hyperbolic Equations; Copyright Page; Dedication; Table of Contents; PREFACE; ACKNOWLEDGEMENTS; INTRODUCTION; CHAPTER I; 1. Normal domains; 2. The causal structure of space-times; 3. Vector bundles; 4. The wave equation for differential forms in non-euclidean spaces; 5. A spinor calculus; Notes and References; CHAPTER II. RIESZ DISTRIBUTIONS; 1. The Riesz distributions in the Minkowski space; 2. The Riesz distribution in curved space-times; 3. Some generalizations; Notes and References; CHAPTER III. THE FUNDAMENTAL SOLUTIONS.

1. The Hadamard coefficients2. B-Series; 3. The fundamental solutions; 4. Applications of the fundamental solutions; 5. The Cauchv problem; Notes and References; CHAPTER IV. HUYGENS' OPERATORS; 1. Hadamard's Criterion; 2. Huygens' triples; 3. Diversors. General wave families; 4. Maxwell's equations. Dirac's equations; Notes and References; CHAPTER V. THE EULER-POISSON-DARBOUX EQUATION; 1. An Application of the Method of Descent; 2. The singular Cauchy problem; 3. Huygens' principle for the EPD-equation; 4. Stellmacher's equations.

5. Elliptic operators with vanishing first Hadamard coefficientAppendix (Proof of Theorem 5.13 (i)); 6. Relations to spectral geometry; Notes and References; CHAPTER VI. TRANSFORMATION THEORY; 1. The bundle connection associated to an operator P; 2. A property of the Hadamard coefficients; 3. Conformai gauge transformations of an operator P; 4. Tensors with simple transformation law; 5. The moments of a normal hyperbolic operator (even dimension); 6. The moments for Maxwell's equations; Notes and References.

CHAPTER VII. SOME THEOREMS ON HUYGENS' OPERATORS OVER FOUR-DIMENSIONAL SPACE-TIMES1. Some preparatory transformations; 2. The moments of order d"3; 3. Applications to Huygens' operators in a four-dimensional space-time; 4. The case of conformally flat metrics; Notes and References; CHAPTER VIII. PLANE WAVE MANIFOLDS AND HUYGENS' PRINCIPLE; 1. Introduction. Results; 2. pp- and plane wave manifolds; 3. Huygens' principle for plane wave manifolds; 4. A characterization of plane wave manifolds; 5. Some conformally invariant tensors; 6. Testing coefficients by pp-metrics.

7. Testing coefficients by metrics of constant curvatureNotes and References; TABLE I: Identities for the Weyl tensor; TABLE II: Moments of order d"4 in four dimensions; TABLE III: Some formulas for pp-metrics; TABLE IV: Some formulas for plane wave metrics; APPENDIX I: METRIC AND CURVATURE IN NORMAL COORDINATES; APPENDIX II: WEAK HUYGENS' OPERATORS By V. Wünsch; APPENDIX III: HUYGENS' PRINCIPLE FOR SPIN TENSOR EQUATIONS By V. Wünsch; INDEX; BIBLIOGRAPHY.