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Specialized Topics in Geometry (ΓΕ8): Διαφορά μεταξύ των αναθεωρήσεων

Specialized Topics in Geometry (ΓΕ8): Διαφορά μεταξύ των αναθεωρήσεων

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* [[Ειδικά Θέματα Γεωμετρίας (ΓΕ8)|Ελληνική Έκδοση]]
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=== General ===
=== General ===
Γραμμή 60: Γραμμή 62:
=== Syllabus ===
=== Syllabus ===


* Bochner’s technique in Differential Geometry.
* Complex manifolds.
* Complex manifolds, Kähler manifolds, Riemann surfaces.
* Kählerian manifolds.
* Isometric and conformal immersions.
* Riemannian submersions and projective spaces.
* Rigidity aspects of isometric immersions.
* Homogeneous and symmetric spaces.
* Minimal submanifolds in Riemannian manifolds.
* Holonomy groups.
* Harmonic maps, geometric PDE’s and flows.
* The Bochner technique.
* Harmonic maps and harmonic forms.
* Minimal submanifolds.
* Convergence of Riemannian manifolds.
* Comparison theorems.
* Geometric flows.


=== Teaching and Learning Methods - Evaluation ===
=== Teaching and Learning Methods - Evaluation ===
Γραμμή 105: Γραμμή 112:


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Τελευταία αναθεώρηση της 16:28, 15 Ιουνίου 2023

General

School School of Science
Academic Unit Department of Mathematics
Level of Studies Graduate
Course Code ΓΕ8
Semester 2
Course Title Special Topics in Geometry
Independent Teaching Activities Lectures (Weekly Teaching Hours: 3, Credits: 7.5)
Course Type Special Background
Prerequisite Courses -
Language of Instruction and Examinations

Greek

Is the Course Offered to Erasmus Students Yes (in English)
Course Website (URL) See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

In this lecture we discuss several topics concerning contemporary topics in Differential Geometry, e.g. symplectic and Kähler manifolds, theory of isometric immersions, minimal surfaces and geometric evolution equations.

General Competences
  • Work autonomously
  • Work in teams
  • Develop critical thinking skills

Syllabus

  • Complex manifolds.
  • Kählerian manifolds.
  • Riemannian submersions and projective spaces.
  • Homogeneous and symmetric spaces.
  • Holonomy groups.
  • The Bochner technique.
  • Harmonic maps and harmonic forms.
  • Minimal submanifolds.
  • Convergence of Riemannian manifolds.
  • Comparison theorems.
  • Geometric flows.

Teaching and Learning Methods - Evaluation

Delivery

Face-to-face

Use of Information and Communications Technology -
Teaching Methods
Activity Semester Workload
Lectures 39
Autonomous Study 78
Solution of Exercises - Homeworks 70.5
Course total 187.5
Student Performance Evaluation

Weakly homeworks, presentations.

Attached Bibliography

  • B. Andrews and C. Hopper, The Ricci flow in Riemannian Geometry, Springer, 2011.
  • T. Colding and W. Minicozzi, A course in minimal surfaces, Graduate Studies in Mathematics, Volume 121, 2011.
  • M. Dajczer and R. Tojeiro, Submanifolds theory beyond an introduction, Springer, 2019.
  • J. Jost, Riemannian Geometry and Geometric Analysis, 7th edition, Springer, 2017.
  • P. Petersen, Riemannian Geometry, 3rd edition, Graduate Texts in Mathematics, 171, Springer, 2016.
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