Classical Differential Geometry II

Course Information
TitleΚΛΑΣΙΚΗ ΔΙΑΦΟΡΙΚΗ ΓΕΩΜΕΤΡΙΑ ΙΙ / Classical Differential Geometry II
Cycle / Level1st / Undergraduate
Teaching PeriodSpring
Course ID40000470

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

Registered students: 21
OrientationAttendance TypeSemesterYearECTS
CoreElective Courses belonging to the selected specializationSpring-5.5

Class Information
Academic Year2017 – 2018
Class PeriodSpring
Faculty Instructors
Weekly Hours3
Class ID
Course Type 2016-2020
  • Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
  • Face to face
Digital Course Content
The course is also offered to exchange programme students.
Language of Instruction
  • Greek (Instruction, Examination)
  • English (Examination)
  • French (Examination)
  • German (Examination)
General Competences
  • Work autonomously
  • Work in teams
  • Work in an international context
  • Work in an interdisciplinary team
  • Generate new research ideas
Course Content (Syllabus)
Elements of the theory of differential forms. The methode of the mooving frame. The fundamental equations of the surfaces theory. Invariant forms. The Gauss mapping. The Darboux frame. Normal curvature, geodesic curvature, geodesic torsion. Principal curvatures. Lines of curvature. Intrinsic surfaces geometry.
Intrinsic surfaces, Cartan's method
Educational Material Types
  • Notes
  • Slide presentations
  • Book
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Communication with Students
Course Organization
Reading Assigment
Student Assessment
Written examination
Student Assessment methods
  • Written Exam with Short Answer Questions (Formative, Summative)
  • Written Assignment (Formative, Summative)
  • Written Exam with Problem Solving (Formative, Summative)
Course Bibliography (Eudoxus)
- Ν. Στεφανίδη: Διαφορική Γεωμετρία, Β’ έκδοση βελτ. και επαυξ. - Ν. Στεφανίδη: Διαφορική Γεωμετρία, Τόμος Ι - Δ.Κουτρουφιώτη: Στοιχεία Διαφορικής Γεωμετρίας, Leader Books, 2006
Additional bibliography for study
- Gray A.: Modern Differential Geometry of Curves and Surfaces with Mathematica. Second edition. CRC Press, 1998 - Haack W.: Elementare Differentialgeometrie. Birkhäuser Verlag, 1955 - Laugwitz D.: Differentialgeometrie. B.G.Teubner, 1977 - Μπρίκα Μ.: Μαθήματα Θεωρίας Επιφανειών. 1967 - Pressley A.: Στοιχειώδης Διαφορική Γεωμετρία. Π.Ε.Κ. 2011 - Στάμου Γ.: Ασκήσεις Διαφορικής Γεωμετρίας. Εκδόσεις Ζήτη, 1990 - Scheffers G..: Anwendung der Differential- und Integralrechnung auf Geometrie. W. d. Gruyter & Co, 1922 - Strubecker K.: Differentialgeometrie, Sammlung Göschen, 1969
Last Update