Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master
SUBJECT

Code	Subject	
MMG1001	Riemannian Geometry	

Section	Semester	Hours: C+S+L	Category	Type	
Mathematics	1	2+2+0	speciality	compulsory	

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
	
Bibliography	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&#8211;V, Publish or Perish, Berkeley, 1979
	
Assessment	Final exam (70%), the activity during the semester (30%)