Geodesics of three-dimensional walker manifolds

Date

2016-07

Editor(s)

Advisor

Ünal, Bülent

Supervisor

Co-Advisor

Co-Supervisor

Instructor

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Abstract

We review some basic facts of Lorentzian geometry including causality and geodesic completeness. We depict the properties of curves and planes in threedimensional Minkowski space. We deffne the Walker manifolds, that is, a Lorentzian manifold which admits a parallel degenerate distribution. We calculate the Christoffel symbols and Levi-Civita connection components, Riemann curvature and Ricci curvature components for an arbitrary three-dimensional Walker manifold and strictly Walker manifold. Finally, we derive the geodesic equations of a three-dimensional Walker manifold and investigate the geodesic curves in it, particularly the ones with a constant component. We prove that any straight line with a constant third component is a geodesic in any Walker manifold with the causality depending on its second component. We prove that the existence of a geodesic in a Walker manifold with a linear third component implies that the manifold is strict. We also show that any three-dimensional Walker manifold is geodesically complete.

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Course

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Book Title

Keywords

Walker manifold, Lorentzian manifold, Geodesic

Degree Discipline

Mathematics

Degree Level

Master's

Degree Name

MS (Master of Science)

Citation

Published Version (Please cite this version)

Language

English

Type