Course Information
TitleΔΙΑΦΟΡΙΣΙΜΕΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΙΙ / Differential Manifolds II
Code0333
FacultySciences
SchoolMathematics
Cycle / Level1st / Undergraduate
Teaching PeriodSpring
CoordinatorFani Petalidou
CommonNo
StatusActive
Course ID40000471

Programme of Study: UPS of School of Mathematics (2014-today)

Registered students: 10
OrientationAttendance TypeSemesterYearECTS
CoreElective Courses belonging to the selected specializationSpring-5.5

Class Information
Academic Year2019 – 2020
Class PeriodSpring
Faculty Instructors
Weekly Hours3
Class ID
600147686
Type of the Course
  • Scientific Area
Course Category
Knowledge Deepening / Consolidation
Mode of Delivery
  • Face to face
Digital Course Content
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
  • Greek (Instruction, Examination)
Prerequisites
Required Courses
  • 0303 Classical Differential Geometry I
  • 0304 Differential Manifolds I
  • 0206 Differential Equations
Learning Outcomes
Deepening on introductory concepts of Riemannian geometry.
General Competences
  • Apply knowledge in practice
  • Work autonomously
  • Work in teams
Course Content (Syllabus)
The notion of the metric and of the isometry map. Theory of connections. the notion of the covariant derivative. Levi-Civita connection. Geodesics. Curvature tensor. Sectional curvature, Ricci curvature and scalar curvature. Hypersurfaces of a Riemannian manifold. Riemannian manifolds of constant curvature. Elements from the theory of smooth manifolds. Riemannian manifolds. Linear connections. Geodesics and curvature. Sectional curvature. Jacobi fields and second fundamental form.
Educational Material Types
  • Notes
  • Book
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Communication with Students
Course Organization
ActivitiesWorkloadECTSIndividualTeamworkErasmus
Lectures1304.3
Seminars
Reading Assigment321.1
Exams30.1
Total1655.5
Student Assessment
Description
Written Examination
Student Assessment methods
  • Written Exam with Short Answer Questions (Formative, Summative)
  • Written Exam with Extended Answer Questions (Formative, Summative)
  • Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
Δημητρίου Κουτρουφιώτη, Διαφορική Γεωμετρία, Πανεπιστήμιο Ιωαννίνων 1994. Ανδρέα Αρβανιτογεώργου, Γεωμετρία Πολλαπλοτήτων – Πολλαπλότητες Riemann και Ομάδες Lie, Ελληνικά Ακαδημαϊκά Ηλεκτρονικά Συγγράμματα και Βοηθήματα, www.kallipos.gr
Additional bibliography for study
M. P. do Carmo, Riemannian Geometry, Birkhäuser 1992. John M. Lee, Riemannian manifolds. An introduction to curvature, GTM 176, Springer-Verlag 1997. Loring W. Tu, An introduction to Manifolds, Universitext, Springer 2011.
Last Update
15-03-2020