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On the Non-Existence of Compact Lorentzian Manifolds with Constant Positive Curvature

Lundberg, David LU (2015) In Master's Theses in Mathematical Sciences MATM01 20152
Mathematics (Faculty of Sciences)
Abstract (Swedish)
In this Master's Thesis we study Semi-Riemannian Geometry. More speci cally, this is done by
discussing some well-known classi cation theorems from Riemannian geometry and then showing
some counter-examples to these in the semi-Riemannian setting. In particular, we brie y discuss
the theorem by Hopf and Rinow, and give a counter-example to this in the semi-Riemannian
setting.
Moreover, we study a well-known and important result by Klingler, which asserts that a compact
Lorentzian manifold of constant sectional curvature must be geodesically complete. We also discuss
a theorem by Calabi and Markus, which together with the theorem by Klingler asserts that in the
Lorentzian setting there can be no compact manifolds of positive... (More)
In this Master's Thesis we study Semi-Riemannian Geometry. More speci cally, this is done by
discussing some well-known classi cation theorems from Riemannian geometry and then showing
some counter-examples to these in the semi-Riemannian setting. In particular, we brie y discuss
the theorem by Hopf and Rinow, and give a counter-example to this in the semi-Riemannian
setting.
Moreover, we study a well-known and important result by Klingler, which asserts that a compact
Lorentzian manifold of constant sectional curvature must be geodesically complete. We also discuss
a theorem by Calabi and Markus, which together with the theorem by Klingler asserts that in the
Lorentzian setting there can be no compact manifolds of positive constant curvature. (Less)
Please use this url to cite or link to this publication:
author
Lundberg, David LU
supervisor
organization
course
MATM01 20152
year
type
H2 - Master's Degree (Two Years)
subject
publication/series
Master's Theses in Mathematical Sciences
report number
LUNFMA-3086-2015
ISSN
1404-6342
other publication id
2015:E45
language
English
id
8891178
date added to LUP
2024-10-11 12:58:59
date last changed
2024-10-11 13:08:10
@misc{8891178,
  abstract     = {{In this Master's Thesis we study Semi-Riemannian Geometry. More speci cally, this is done by
discussing some well-known classi cation theorems from Riemannian geometry and then showing
some counter-examples to these in the semi-Riemannian setting. In particular, we brie y discuss
the theorem by Hopf and Rinow, and give a counter-example to this in the semi-Riemannian
setting.
Moreover, we study a well-known and important result by Klingler, which asserts that a compact
Lorentzian manifold of constant sectional curvature must be geodesically complete. We also discuss
a theorem by Calabi and Markus, which together with the theorem by Klingler asserts that in the
Lorentzian setting there can be no compact manifolds of positive constant curvature.}},
  author       = {{Lundberg, David}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{On the Non-Existence of Compact Lorentzian Manifolds with Constant Positive Curvature}},
  year         = {{2015}},
}