DIFFERENTIAL GEOMETRY
DIFFERENTIAL GEOMETRY
A.Y. | Credits |
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2023/2024 | 8 |
Lecturer | Office hours for students | |
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Giovanni Molica Bisci | Monday 14-16 or by appointment |
Teaching in foreign languages |
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Course entirely taught in a foreign language
English
This course is entirely taught in a foreign language and the final exam can be taken in the foreign language. |
Assigned to the Degree Course
Date | Time | Classroom / Location |
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Date | Time | Classroom / Location |
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Learning Objectives
Aim of the course is to give to the students some basic tools and topics in Riemmannian Geometry.
Program
1. Preliminaries
1.1. General topology
1.2. Algebraic topology
1.3. Multivariable analysis
1.4. Projective geometry
2. Tensors
2.1. Multilinear algebra
2.2. Tensors
2.3. Scalar products
2.4. The symmetric and exterior algebras
2.5. Grassmannians
2.6. Orientation
3. Smooth manifolds
3.1. Smooth manifolds
3.2. Smooth maps
3.3. Partitions of unity
3.4. Tangent space
3.5. Smooth coverings
3.6. Orientation
3.7. Submanifolds
3.8. Immersions, embeddings, and submersions
3.9. Examples
3.10. Homotopy and isotopy
3.11. The Whitney embedding
Bridging Courses
There are no mandatory prerequisites.
Learning Achievements (Dublin Descriptors)
Knowledge and understanding: at the end of the course the student will learn the basic notions of Riemmannian Geometry.
Applying knowledge and understanding: at the end of the course the student will learn the methodologies of Riemmannian Geometry and will be able to apply them to the study of various problems.
Making judgements: at the end of the course the student will be able to apply the techniques of Riemmannian Geometry in order to solve new problems, also coming from real-world applications.
Communications skills: at the end of the course the student will have the ability to express the fundamental notions of Riemmannian Geometry using a rigorous terminology.
Learning skills: during the course the student will learn the ability to study the notions of Riemmannian Geometry, also in order to use it in solving different kind of problems.
Teaching Material
The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it
Teaching, Attendance, Course Books and Assessment
- Teaching
Theorical and practical lessons.
- Attendance
Although strongly recommended, course attendance is not mandatory.
- Course books
M. Abate and F. Tovena, Geometria differenziale, Springer–Verlag, 2011.
M. Lee, Riemannian manifolds, Graduate Texts in Mathematics, vol. 176, Springer, 1997.
M. Spivak, A comprehensive introduction to differential geometry. Vol. III and Vol. V, Publish or Perish, 1979.
- Assessment
The exam of Differential Geometry consists of a written exam on the topics of the course.
- Disabilità e DSA
Le studentesse e gli studenti che hanno registrato la certificazione di disabilità o la certificazione di DSA presso l'Ufficio Inclusione e diritto allo studio, possono chiedere di utilizzare le mappe concettuali (per parole chiave) durante la prova di esame.
A tal fine, è necessario inviare le mappe, due settimane prima dell’appello di esame, alla o al docente del corso, che ne verificherà la coerenza con le indicazioni delle linee guida di ateneo e potrà chiederne la modifica.
Additional Information for Non-Attending Students
- Teaching
As for attending students.
- Attendance
As for attending students.
- Course books
As for attending students.
- Assessment
As for attending students.
- Disabilità e DSA
Le studentesse e gli studenti che hanno registrato la certificazione di disabilità o la certificazione di DSA presso l'Ufficio Inclusione e diritto allo studio, possono chiedere di utilizzare le mappe concettuali (per parole chiave) durante la prova di esame.
A tal fine, è necessario inviare le mappe, due settimane prima dell’appello di esame, alla o al docente del corso, che ne verificherà la coerenza con le indicazioni delle linee guida di ateneo e potrà chiederne la modifica.
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