Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT
| MMG1001 | Riemannian Geometry |
| Teaching Staff in Charge |
Assoc.Prof. BLAGA Paul Aurel, Ph.D., pablaga cs.ubbcluj.ro |
| Aims |
|
The goal of the course is to familiarize the students with the main notions and results from Riemannian Geometry, a multi-dimensional generalization of the differential geometry of surfaces from the three-dimensional Euclidean space. |
| Content |
|
1. A review of the basic notions and results from the theory of smooth manifolds
2. Tensor calculus and differential forms 3. Riemannian metrics 4. Linear connexions. The Levi-Civita connection 5. Geodesics and the exponential mapping 6. The riemannian manifolds as metric spaces. The Myers-Steenrod and Hopf-Rinow theorems 7. The curvature of riemannian manifolds 8. Riemannian submanifolds 9. The Gauss-Bonnet theorem |
| References |
|
1. Blaga, P.A.: Lectures on Classical Differential Geometry, Risoprint, Cluj
Napoca, 2005, 2. Boothby, W.: An Introduction to Differentiable Manifolds and Riemannian Geometry (edi¸tia a II-a), Academic Press, New York, 1985 3. do Carmo, M.: Riemannian Geometry, Birkhauser, 1992 4. Darling, R.W.R.: Differential Forms and Connections, Cambridge University Press, Cambridge, 1994 5. Gallot, S., Hulin, D., Lafontaine, J.: Riemannian Geometry (ed. III), Springer, 2004 6. Ianus, S.: Geometrie diferentiala cu aplicatii în teoria relativitatii, Editura Academiei, Bucure¸sti, 1982 7. Lee, J.: Riemannian Geometry, Springer, 1997 8. Singer, I.M., Thorpe, J.A.: Lecture Notes on Elementary Topology and Geometry, Scott, Foresman and Co., 1967 9. Spivak, M.: A Comprehensive Introduction to Differential Geometry, vols. I–V, Publish or Perish, Berkeley, 1979 |
| Assessment |
|
Final exam (70%), the activity during the semester (30%) |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |