Pseudo-Riemannian manifolds with common geodesics

Abstract

CONTENTSIntroductionChapter I. Projective connections and projective mappings §1. Affine mappings §2. The projective structure §3. Projectively equivalent affine connections §4. Projective mappingsChapter II. Projectively equivalent Riemannian connections §1. Definition of a skew-normal frame §2. Structure equations in a skew-normal frame §3. Forms of Riemannian connections with common geodesies in a skew-normal frameChapter III. Pseudo-Riemannian metrics with common geodesies §1. The technique of integration in a skew-normal frame. The case of simple roots §2. The general caseChapter IV. Pseudo-Riemannian metrics with general connections §1. The forms for affinely equivalent Riemannian connections in a skew-normal frame §2. The concept of the index of the characteristic of a parallel bilinear form. Diagram technique §3. Lorentz manifoldsConclusionReferences