GEOMETRY III
Academic year and teacher
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- Versione italiana
- Academic year
- 2017/2018
- Teacher
- MASSIMILIANO MELLA
- Credits
- 10
- Didactic period
- Annualità Singola
- SSD
- MAT/03
Training objectives
- The course furnishes advanced tools in the study of differential varieties. Together with the learning of the techniques the student is encouraged to study the same object from different viewpoints.
Prerequisites
- It is recommended to attend courses in:-linear algebra-topology-calculus
Course programme
- The course is strctured in two parts of 56 and 24 hours.
The first part is Differential geometry.
Differentiable varieties, embedding theorems, tabgent bundle and derivations (30 hours)
Frobenius Theorem, distributions and vector bundles (15 hours)
Differentiable surfaces, second fundamental form and Gaussian curvature (11 hours).
The second part is dedicated to projective geometry.
Projective spaces - linear subspaces - conics and quadrics (20 hours)
Projective viewpoint on the second fundamental form, classification of surfaces iwth zero Gaussian curvature ( 4 hours) Didactic methods
- Lectures and example classes. Every 4 hours of lecture there are 2 hours of example classes where students are asked to participate in exercise solutions.
Learning assessment procedures
- At the end of each module there is an example sheet that student has to prepare at home, without marking.
The exam is composed by:
a written test of one hour and a half with questions and exercises on the first part (each question has his own marking),
an oral exam where the student has to solve exercises at the blackboard on the second part.
The final marking is given according to both oral presentation and the written marking. Reference texts
- E. Sernesi "Geometria 1" "Geometria 2" Bollati BoringhieriAddison-Wesley
M. do Carmo "Differential geometry of curves and surfaces" Prentice Hall
Lecture notes
