Course Details for A.Y. 2017/2018
Name:
Geometria Superiore 2 mod. I / Geometria Superiore 2 mod. I
Basic information
Credits:
: Master Degree in Mathematics 6 CFU (c)
Degree(s):
Master Degree in Mathematics 2nd anno curriculum Generale Elective
Language:
Italian
![[info]](img/info16.png)
Course Objectives
Si prevede che lo studente acquisisca le nozioni di base di geometria Riemanniana e sia in grado di usare gli strumenti acquisiti per risolvere problemi su tale tema.
Course Content
- Differentiable manifolds. Riemannian metrica. Affine and riemannian connection.
Geodesics and convex neighborhood. Curvatures. Jacobi fields. Isometric Immersions.
Complete manifolds. Hopf-Rinow Theorem and Hadamard theorem.
Learning Outcomes (Dublin Descriptors)
On successful completion of this course, the student should
- The student should have knowledge of the basic theory of Riemannian geometry and develop some
topic of this theory.
- The student should be able to solve problems about Riemannian geometry.Moreover the student should be able to recognize when the acquired notions ofRiemannian geometry are necessary to the comprehension of other topics.
- The student should be able to understand problems of riemannian geometry
and recognize the best method to solve them.
- The student should be able to explain the statements and the proofs of the theorems about riemannian manifolds.
- The student should have acquired the ability of reading and understanding advanced text
of riemannian geometry
Prerequisites and Learning Activities
Basic notions of differential geometry and analysis in several variables.
Assessment Methods and Criteria
homework and oral exam
Textbooks
- M. P. Do Carmo, Riemannian Geometry , Birkhauser.
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: 11 febbraio 2014, 17:54
Italian version
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