On the fundamental group of a complete globally hyperbolic Lorentzian manifold with a lower bound for the curvature tensor

TL;DR

This paper investigates the fundamental group of certain globally hyperbolic Lorentzian manifolds with positive curvature, proving finiteness under specific completeness and compactness conditions.

Contribution

It establishes the finiteness of the fundamental group for lightlike geodesically complete Lorentzian products with positive curvature tensor and compact fiber.

Findings

Fundamental group is finite under given conditions.

Lightlike geodesic completeness implies topological restrictions.

Positive curvature tensor influences the manifold's topology.

Abstract

In this paper, we study the fundamental group of a certain class of globally hyperbolic Lorentzian manifolds with a positive curvature tensor. We prove that the fundamental group of lightlike geodesically complete parametrized Lorentzian products is finite under the conditions of a positive curvature tensor and the fiber compact.