On the Non-Existence of Compact Lorentzian Manifolds with Constant Positive Curvature
(2015) In Master's Theses in Mathematical Sciences MATM01 20152Mathematics (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:
http://lup.lub.lu.se/student-papers/record/8891178
- author
- Lundberg, David LU
- supervisor
- organization
- course
- MATM01 20152
- year
- 2015
- 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}}, }