Advanced Differential Geometry I

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

Differential Geometry 1,2

Course Contents

Curves in Rn, Tangent vectors, Vector fields, Directional derivatives, Covariant derivatives, Arc-lenght function, Frenet Formulas, Geometries of curves, Curvature circle, curvature axes, curvature sphere, geometry of surface in Rn, Weingarten Map and Shape Operator, Gauss Map and Principle forms, curvatures of surfaces, curves on surface, Gauss-Bonnet, Theory of manifolds.

Weekly Schedule

1) Curves in Rn
2) Tangent vectors
3) Vector fields
4) Directional derivatives
5) Covariant derivatives
6) Arc-lenght function
7) Frenet Formulas, Curvature circle, curvature axes, curvature sphere,
8) Midterm examination/Assessment
9) geometry of surface in Rn
10) Weingarten Map and Shape Operator
11) Gauss Map and Principle forms
12) Curvatures of surfaces
13) Curves on surface
14) Gauss-Bonnet Theorem
15) Theory of manifolds
16) Final examination

Recommended or Required Reading

Planned Learning Activities and Teaching Methods

1) Lecture
2) Lecture
3) Lecture
4) Question-Answer
5) Question-Answer
6) Question-Answer
7) Discussion
8) Discussion
9) Discussion
10) Drill and Practice
11) Drill and Practice
12) Drill and Practice
13) Brain Storming
14) Brain Storming
15) Brain Storming
16) Self Study
17) Self Study
18) Self Study
19) Problem Solving
20) Problem Solving
21) Problem Solving

Assessment Methods and Criteria

Contribution of Midterm Examination to Course Grade	40%
Contribution of Final Examination to Course Grade	60%
Total	100%

Language of Instruction

Turkish

Work Placement(s)

Not Required