Information Package / Course Catalogue
Differential Geometry II
Course Code: MAT417
Course Type: Area Elective
Couse Group: First Cycle (Bachelor's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 2
Prt.: 2
Credit: 3
Lab: 0
ECTS: 6
Objectives of the Course

The fundamental knowledges that are needed during students undergraduate and graduate education on differential geometry are taught.

Course Content

Osculating hyperplanes of curves, curves, center of curvature, frame structures, pairs of curves, orientation on hypersurfaces, shape operator, fundamental forms, Riemann curvature tensor, hypersurfaces

Name of Lecturer(s)
Lec. Dilek AÇIKGÖZ KAYA
Learning Outcomes
1.Defines hyperplane of a curve
2.Explains the curvature in a geometric manner
3.Defines frame structures
4.Defines and compares some curve pairs
5.Explains the orientation of hypersurfaces
6.Calculates shape operator and fundamental forms
7.Calculates and expounds Riemann curvature tensor
Recommended or Required Reading
1.Eğrilerin ve Yüzeylerin Diferensiyel Geometrisi, Prof. Dr. Cumali Ekici
2.Elementary Differential Geometry, Barret O’Neill
3.Diferansiyel Geometri (Differantial Geometry), Prof. Dr. Arif Sabuncuoğlu
Weekly Detailed Course Contents
Week 1 - Theoretical & Practice
Osculating hyperplanes of the curve
Week 2 - Theoretical & Practice
Curvatures and their geometric meanings
Week 3 - Theoretical & Practice
Centers of curvature and osculating spheres
Week 4 - Theoretical & Practice
Bishop frame structures
Week 5 - Theoretical & Practice
q-frames along the space curves
Week 6 - Theoretical & Practice
Parallel curve pair, involute and evolute curve
Week 7 - Theoretical & Practice
Bertrand curve pair, Mannheim curve pair, natural partner curve
Week 8 - Theoretical & Practice
Orientation on hypersurfaces (Midterm Exam)
Week 9 - Theoretical & Practice
Shape operator
Week 10 - Theoretical & Practice
Fundamental forms
Week 11 - Theoretical & Practice
Algebraic invariants of the shape operator
Week 12 - Theoretical & Practice
Riemann curvature tensor
Week 13 - Theoretical & Practice
Curvature line, asymptotic line and their directions
Week 14 - Theoretical & Practice
Some hypersurfaces
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%40
Final Examination1%60
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory140228
Lecture - Practice140228
Individual Work140456
Midterm Examination111213
Final Examination123225
TOTAL WORKLOAD (hours)150
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
PÇ-16
PÇ-17
PÇ-18
OÇ-1
3
4
3
4
2
OÇ-2
4
2
4
3
OÇ-3
4
3
4
3
3
OÇ-4
4
3
4
3
3
OÇ-5
4
2
4
4
4
OÇ-6
4
4
4
3
OÇ-7
4
3
3
2
Adnan Menderes University - Information Package / Course Catalogue
2026