Classical Differential Geometry I

Course Information
TitleΚΛΑΣΙΚΗ ΔΙΑΦΟΡΙΚΗ ΓΕΩΜΕΤΡΙΑ Ι / Classical Differential Geometry I
Cycle / Level1st / Undergraduate
Teaching PeriodWinter
Course ID40000467

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

Registered students: 3
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course537

Class Information
Academic Year2015 – 2016
Class PeriodWinter
Faculty Instructors
Weekly Hours5
Class ID
Type of the Course
  • Scientific Area
Course Category
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)
Required Courses
  • 0301 Analytic Geometry I
  • 0302 Analytic Geometry II
Learning Outcomes
Deeping and understanding of basic concepts of Classical Differential Geometry.
General Competences
  • Work autonomously
  • Work in teams
  • Work in an international context
  • Work in an interdisciplinary team
  • Generate new research ideas
Course Content (Syllabus)
Theory of Curves: The concept of the curve in the differential geometry. The mooving frame. The Frenet' s formalae. The fundamental theorem (existence and uniqueness). Osculating sphere and osculating cyrcle. Special curves. Plane curves. Surfaces theory: The concept of the surface in the differential geometry. Curves on a surface. The first and the second fundamental form. Asymptotic lines. Christoffel' s symbols. Equations of Gauss and Weingarten. Theorema Egregium of Gauss. The fundamental theorem (existence and uniqueness).
Theory of curves, theory of surfaces
Educational Material Types
  • Notes
  • 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)
- Σ. Σταματάκη: Εισαγωγή στην Κλασική Διαφορική Γεωμετρία, εκδόσεις Αϊβάζη - Ν. Στεφανίδη: Διαφορική Γεωμετρία, Β’ έκδοση βελτ. και επαυξ. - Ν. Στεφανίδη: Διαφορική Γεωμετρία, Τόμος Ι
Additional bibliography for study
- do Carmo M. P.: Differential Geometry of Curves and Surfaces. Prentice – Hall, 1976 - Giering O., Hoschek J.: Geometrie und ihre Anwendungen. Carl Heuser Verlag, 1994. - Gray A.: Modern Differential Geometry of Curves and Surfaces with Mathematica. Second edition. CRC Press, 1998 - Haack W.: Elementare Differentialgeometrie. Birkhäuser Verlag, 1955 - Hsiung C. C.: A first Course in Differential Geometry. John Wiley & Sons, 1981 - Kreyszig E.: Differential Geometry. University of Toronto Press, 1959 - Laugwitz D.: Differentialgeometrie. B.G.Teubner, 1977 - Lelong-Ferrand J., Arnaudiés J.M.: Cours de Mathématiques. Tome 3, Géometrie et cinématique. Dunod, 1977 - Oprea J.: Differential Geometry and its Applications. Prentice Hall, 1997 - Παπαντωνίου Β.: Διαφορική Γεωμετρία, 1997 - 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
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