Course Details for A.Y. 2018/2019
Name:
Geometria Riemaniana / Riemannian Geometry
Basic information
Credits:
: Master Degree in Mathematics 6 CFU (c)
Degree(s):
Master Degree in Mathematics 2nd anno curriculum Generale Elective
Language:
English
![[info]](img/info16.png)
Course Objectives
The objective of this course is to get the student familiar with basic notions and some fundamental results of Riemannian Geometry .
At the end of the course the student should be able to solve by her/him-self some simple, but new problems regarding all the program.
Course Content
- Differentiable manifolds
- Riemannian Metrics
- Affine and Riemannian connections
- Geodesics, curvatures
- Jacobi Fields
- Isometric Immersions
- Complete manifolds: Hopf and Hadamard theorems
- Constan curvature spaces
- Variations of energy
Learning Outcomes (Dublin Descriptors)
On successful completion of this course, the student should
-
- Know the basic notions and the fundamental results of Riemannian geometry
- Be able to solve simple problems regarding the program.
- Be able to select which problems they can discuss and understand with the notions they have.
- Organize the notions they have acquired with different points of view, to get new (even if not original) results.
Prerequisites and Learning Activities
Analysis of one and many variables, linear algebra, geometry of curves and surfaces, basic topology.
Assessment Methods and Criteria
Written and Oral
Textbooks
- M.P. Do Carmo, Riemannian Geometry , Birkhauser. 1992.
- P. Petersen, Riemannian Geometry , Springer 2016.
Notes
- The objective of the course is to give the basic notion Riemannian Geoemtry and to be able to understand some fundamental results of the subject.
Course page updates
This course page is available (with possible updates) also for the following academic years:
To read the current information on this course, if it is still available, go to the university course catalogue .
Course information last updated on: 31 maggio 2019, 16:07
Italian version
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