MAT6024 Advanced Differential Geometry IIBahçeşehir UniversityDegree Programs MATHEMATICS (TURKISH, PHD)General Information For StudentsDiploma SupplementErasmus Policy StatementNational Qualifications
MATHEMATICS (TURKISH, PHD)
PhD. TR-NQF-HE: Level 8 QF-EHEA: Third Cycle EQF-LLL: Level 8

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT6024 Advanced Differential Geometry II Spring 3 0 3 8
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Prof. Dr. ERTUĞRUL ÖZDAMAR
Recommended Optional Program Components: None
Course Objectives: The object of the course is to provide basic concepts to students,of complex structures, holomorphic transformations, Hermitian and Kähler metrics, Riemannian manifolds and Kähler manifolds.

Learning Outcomes

The students who have succeeded in this course;
The students who succeeded in this course;
o will be able to know the concepts of complex structures and holomorphic maps and do basic calculations about them.
o will be able to know Hodge and Dolbeault theories.
o will be able to apply concepts of Complex and holomorphic vector bundles and Hermitian bundles
o will be able to give examples of Kähler metrics
o will be able to use natural operators on Riemannian and Kähler manifolds and the Ricci form of Kahler manifolds

Course Content

Complex structures and holomorphic maps
Holomorphic forms and vector fields
Complex and holomorphic vector bundles
Hermitian bundles
Hermitian and Kähler metrics
The curvature tensor of Kähler manifolds
Examples of Kähler metrics
Natural operators on Riemannian and Kähler manifolds
Hodge and Dolbeault theories
The Ricci form of Kahler manifolds
Kahler–Einstein metrics

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Complex structures and holomorphic maps
2) Complex structures and holomorphic maps
3) Holomorphic forms and vector fields
4) Holomorphic forms and vector fields
5) Complex and holomorphic vector bundles
6) Complex and holomorphic vector bundles
7) Hermitian bundles
8) Hermitian and Kähler metrics
9) The curvature tensor of Kähler manifolds
10) Examples of Kähler metrics
11) Natural operators on Riemannian and Kähler manifolds
12) Hodge and Dolbeault theories
13) The Ricci form of Kahler manifolds
14) Kahler–Einstein metrics

Sources

Course Notes / Textbooks: Lectures on Kähler Geometry
By Andrei Moroianu
References: .

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Attendance 14 % 10
Homework Assignments 1 % 10
Midterms 1 % 35
Final 1 % 45
Total % 100
PERCENTAGE OF SEMESTER WORK % 55
PERCENTAGE OF FINAL WORK % 45
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Study Hours Out of Class 3 30 90
Homework Assignments 1 20 20
Midterms 1 20 20
Final 1 20 20
Total Workload 192

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution