Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Author:
Ntoulios Georgios
Supervisors info:
Διονύσιος Λάππας, Αναπληρωτής Καθηγητής, Τμήμα Μαθηματικών, Εθνικόν και Καποδιστριακόν Πανεπιστήμιον Αθηνών
Original Title:
Splitting Theorems for Semi-Riemannian Manifolds
Translated title:
Splitting Theorems for Semi-Riemannian Manifolds
Summary:
In 1971, Cheeger and Gromoll proved that a complete RIemannian manifolds which contains a line is isometric to a Cartesian product of manifolds of smaller dimentions.
The Cheeger-Gromoll splitting theorem was later proved by Eschenburg and Heintze using more elementary methods.
Analogous results were proved for the case of Lorentzian manifolds by Eschenburg, Galloway, Newman and others.
In the first chapter we present some introductory elements of semi-Riemannian manifolds, focusing on the Riemannian and Lorentzian cases.
In the second chapter we present firstly the Cheeger-Gromoll theorem as proved by Eschenburg and Heintze.
In the second half of the second chapter we present a splitting theorem for Lorentzian manifolds. This splitting is as stated by Eschenburg, but we will prove it using some elements from Galloway's proof.
Main subject category:
Science
Keywords:
Splitting Theorem, Riemann manifolds, Lorentz manifolds
