Differenrial Manifolds

Course Information
TitleΘΕΩΡΙΑ ΔΙΑΦΟΡΙΣΙΜΩΝ ΠΟΛΛΑΠΛΟΤΗΤΩΝ / Differenrial Manifolds
Code0658
FacultySciences
SchoolMathematics
Cycle / Level2nd / Postgraduate
Teaching PeriodWinter
CoordinatorFani Petalidou
CommonNo
StatusActive
Course ID40000046

Programme of Study: PMS Tmīmatos Mathīmatikṓn (2018-sīmera)

Registered students: 4
OrientationAttendance TypeSemesterYearECTS
THEŌRĪTIKA MATHĪMATIKACore Courses A31110

Class Information
Academic Year2018 – 2019
Class PeriodWinter
Faculty Instructors
Weekly Hours3
Class ID
600125735
Type of the Course
  • Scientific Area
Course Category
Specific Foundation / Core
Mode of Delivery
  • Face to face
Digital Course Content
Language of Instruction
  • Greek (Instruction, Examination)
  • English (Instruction, Examination)
  • French (Instruction, Examination)
Prerequisites
General Prerequisites
Calculus. Linear Algebra. Group Theory. Differentiable Manifolds I and II
General Competences
  • Apply knowledge in practice
  • Work autonomously
  • Work in teams
  • Work in an interdisciplinary team
Course Content (Syllabus)
Differentiable Manifolds (basic concepts). Fibre bundles. Covectors and 1-forms. Flow of a vector field and integral curves. Distributions. Frobenius theorem. Integral submanifolds. Basic concepts of foliations. Lie groups and Lie algebras (geometric consideration). Invariant vector fields. Integrations of Lie algebras and the exponential map. Examples. Riemannian Metrics. Linear connections. Geodesics. Curvature. Riemannian submanifolds. Complete manifolds. Manifolds of constant curvature.
Educational Material Types
  • Notes
  • Book
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Course Teaching
  • Use of ICT in Communication with Students
Course Organization
ActivitiesWorkloadECTSIndividualTeamworkErasmus
Lectures1605.3
Seminars200.7
Reading Assigment1153.8
Exams50.2
Total30010
Student Assessment
Description
Seminaires. Written Examination.
Student Assessment methods
  • Written Assignment (Formative, Summative)
  • Oral Exams (Formative)
  • Performance / Staging (Formative)
  • Written Exam with Problem Solving (Formative, Summative)
Bibliography
Additional bibliography for study
1) Loring W. Tu, An introduction to Manifolds, Universitext, Springer 2011. 2) John M. Lee, Introduction to Smooth Manifolds, GTM 218, Springer 2003. 3) D. Barden and Ch. Thomas, An Introduction to Differential Manifolds, Imperial College Press, 2003. 4) Lawrence Conlon, Differentiable Manifolds, Second Edition, Modern Birkhäuser Classics, Birkhäuser Boston, Inc., Boston, MA, 2008. 5) Frank W. Warner, Foundations of Differentiable Manifolds and Lie Groups, Graduate Texts in Mathematics, 94, Springer-Verlag, New York-Berlin, 1983.
Last Update
12-09-2019