Information Package / Course Catalogue
Differantial Geometry of Curves and Surfaces
Course Code: MTK535
Course Type: Area Elective
Couse Group: Second Cycle (Master's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 6
Objectives of the Course

The purpose of this course is to learn some theories and applications of differential geometry and also the main theories of the differential geometry of curves and surfaces with using the basic concepts and the techniques of differential geometry.

Course Content

Theory of Surfaces, Hypersurfaces, Shape Operator, Riemann Curvature Tensor, Some Hypersurfaces and Their Properties, Geodesics on Hypersurfaces.

Name of Lecturer(s)
Learning Outcomes
1.Ability to learn routing in hypersurfaces
2.Ability to do some applications with Shape Operator and Fundamental Forms
3.Ability to calculate Riemann Curvature Tensor
4.Ability to determine direction of Line of Curvature and Asymptotic line
5.Ability to learn some properties about hypersurfaces
Recommended or Required Reading
1.Ekici, C., Eğrilerin ve Yüzeylerin Diferensiyel Geometrisi
2.Montiel S., Ros A., Curves and Surfaces
3.O’Neil, B., Elementary Differential Geometry
4.Hacısalihoğlu, H. H., Diferensiyel Geometri, Cilt I-II-III
Weekly Detailed Course Contents
Week 1 - Theoretical
Basic Concepts
Week 2 - Theoretical
Routing in Hypersurfaces
Week 3 - Theoretical
Shape Operator
Week 4 - Theoretical
Fundamental Forms
Week 5 - Theoretical
Solve Problems
Week 6 - Theoretical
Riemann Curvature Tensor
Week 7 - Theoretical
Line of Curvature and Asymtotic Line
Week 8 - Theoretical
Some Hypersurfaces (MIDTERM EXAM)
Week 9 - Theoretical
Regle Surface, Parallel Hypersurfaces
Week 10 - Theoretical
Solve Problems
Week 11 - Theoretical
Geodesics on Hypersurfaces
Week 12 - Theoretical
Asymptotic Lines
Week 13 - Theoretical
Lines of Curvature
Week 14 - Theoretical
Solve Problems
Assessment Methods and Criteria
Type of AssessmentCountPercent
Assignment1%5
Quiz1%10
Midterm Examination1%15
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory141356
Assignment1066
Individual Work140228
Quiz110111
Midterm Examination120222
Final Examination125227
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
OÇ-1
3
2
3
4
2
2
2
2
2
OÇ-2
3
4
4
3
4
4
3
3
4
2
3
4
OÇ-3
3
3
4
4
3
OÇ-4
4
4
3
3
4
4
4
5
OÇ-5
4
4
4
4
3
4
4
4
3
2
2
3
4
Adnan Menderes University - Information Package / Course Catalogue
2026