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

The concept of surfaces, differentiable functions between surfaces, vector fields on surfaces, shape operator, fundamental forms, Riemann curvature tensor, hypersurfaces

Name of Lecturer(s)
Learning Outcomes
1.To be able to define and analyze tangent spaces, normal vector fields, and differentiable functions on surfaces using local parametrizations of surfaces.
2.To be able to compute and interpret operations such as directional derivatives, covariant derivatives, and Lie brackets of vector fields defined on surfaces.
3.To be able to obtain the first and second fundamental forms of a surface using the Gauss map and to compute arc lengths and surface areas.
4.To be able to compute Gaussian and mean curvatures, analyze the local geometric properties of surfaces, and distinguish lines of curvature, geodesics, and asymptotic curves.
5.To be able to analyze the intrinsic and extrinsic geometric structures of surfaces using the induced connection and the Gauss equation, and to classify ruled surfaces.
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
Surfaces
Week 2 - Theoretical & Practice
Monge Surfaces and Surfaces of Revolution
Week 3 - Theoretical & Practice
Tangent Spaces of Surfaces, Related Theorems and Differentiable Functions on Surfaces
Week 4 - Theoretical & Practice
Directional Derivatives on a Surface, Vector Fields on a Surface, Normal Vector Fields of a Surface, and Covariant Derivatives on a Surface
Week 5 - Theoretical & Practice
Shape operator
Week 6 - Theoretical & Practice
Gauss map
Week 7 - Theoretical & Practice
The First Fundamental Form, Arc Length, and Area of Surfaces
Week 8 - Theoretical & Practice
Gaussian Curvature and Mean Curvature of a Surface (Midterm Exam)
Week 9 - Theoretical & Practice
Lines of Curvature, Asymptotic Curves, and Geodesics
Week 10 - Theoretical & Practice
Induced Connection on Surfaces, the Gauss Equation, and Ruled Surfaces
Week 11 - Theoretical & Practice
Lie Bracket of Vector Fields on a Surface
Week 12 - Theoretical & Practice
Riemann curvature tensor
Week 13 - Theoretical & Practice
Hypersurfaces
Week 14 - Theoretical & Practice
Hypersurfaces
Assessment Methods and Criteria
Type of AssessmentCountPercent
Assignment1%5
Term Assignment1%5
Midterm Examination1%30
Final Examination1%60
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory140228
Lecture - Practice140228
Assignment1055
Term Project1099
Individual Work140342
Midterm Examination115217
Final Examination119221
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
Adnan Menderes University - Information Package / Course Catalogue
2026