Course Name Code Semester T+U Hours Credit ECTS
Complex Manifolds II MAT 628 0 3 + 0 3 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level Doctorate Degree
Course Type Optional
Course Coordinator Doç.Dr. MAHMUT AKYİĞİT
Course Lecturers
Course Assistants
Course Category
Course Objective The kahler structures and manifolds course aims to give the fundamental knowledge for the studies of graduate students who study at topology, algebra and geometry branch
Course Content Hermit manifolds, Hermitian structures and connections, Kahler ıdentities, Kahler metrics characterization of kahler metrics, Kahler form and volume, Differential operators on a kahler manifold, Hodge theory on kahler manifolds, The hodge decomposition theorem on compact kahler manifolds, The curvature tensor of kahler manifolds, Almost kahler manifolds, The hodge-riemann bilinear relations on a kahler manifold, Quaternion kahler manifolds, Submanifolds of kahler manifolds, Cr-submanifolds of kahler manifolds
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/she learns hermit manifolds Lecture, Question-Answer, Discussion, Brain Storming, Self Study, Problem Solving, Testing, Homework,
2 He/she realizes Kahler metric and solves its examples Lecture, Question-Answer, Discussion, Brain Storming, Self Study, Problem Solving, Testing, Homework,
3 He/she realizes cuvatures tensors of kahler manifolds Lecture, Question-Answer, Discussion, Brain Storming, Self Study, Problem Solving, Testing, Homework,
4 He/she defines and compares submanifolds of kahler manifolds Lecture, Question-Answer, Discussion, Brain Storming, Self Study, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Hermit manifolds
2 Hermitian structures and connections
3 Kahler ıdentities
4 Kahler metrics characterization of kahler metrics
5 Kahler form and volume
6 Differential operators on a kahler manifold
7 Hodge theory on kahler manifolds
8 The hodge decomposition theorem on compact kahler manifolds
9 The curvature tensor of kahler manifolds
10 Almost kahler manifolds
11 The hodge-riemann bilinear relations on a kahler manifold
12 Quaternion kahler manifolds
13 Submanifolds of kahler manifolds
14 Cr-submanifolds of kahler manifolds
Resources
Course Notes 1.) Daniel Huybrechts, Complex geometry, Springer, 1965.<br>2.) Kunihiko Kodaira, Complex manifold and deformation of complex structures, Springer, 1981.
Course Resources
Order Program Outcomes Level of Contribution
1 2 3 4 5
0 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 70
1. Kısa Sınav 10
1. Ödev 10
2. Ödev 10
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 10 10
Quiz 1 10 10
Assignment 2 16 32
Final examination 1 10 10
Total Workload 158
Total Workload / 25 (Hours) 6.32
dersAKTSKredisi 6