Lie algebras of infinitesimal projective transformations of Lorentz manifolds

Abstract

Contents Introduction Chapter I. Infinitesimal projective transformations §1. Infinitesimal affine transformations §2. Infinitesimal conformal transformations §3. Infinitesimal projective transformations §4. Groups of projective transformations Chapter II. Projective and affine transformations determined by concircular vector fields §1. Conformal and projective Lie algebras determined by concircular vector fields §2. Projective Lie algebras determined by concurrent and parallel vector fields §3. Lie algebras of conformal and projective motions in spaces of constant curvature Chapter III. Lorentz manifolds admitting projective and affine motions §1. The skew-normal frame §2. Integration of the Eisenhart equations, h-spaces §3. The properties of h-spaces. Ordinary h-spaces and K-spaces §4. Non-homothetic projective motions in ordinary h-spaces Chapter IV. Classification of Lorentz manifolds with respect to the Lie algebras of projective and affine motions §1. Lie algebras of projective motions of ordinary h-spaces. The general case §2. Lie algebras of projective motions of ordinary h-spaces of type [I(I...I)] §3. Lie algebras of projective motions of ordinary h-spaces of type [3] §4. On K-spaces and the spaces V(K) §5. Lie algebras of projective motions of spaces V(0) with Lorentz signature §6. Lie algebras of projective motions of spaces V(K) with Lorentz signature §7. Lie algebras of affine motions of Lorentz manifolds Conclusion Bibliography