Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
---|---|---|---|---|---|
Complex Manifolds II | MAT 628 | 0 | 3 + 0 | 3 | 6 |
Ön Koşul Dersleri | |
Önerilen Seçmeli Dersler | |
Dersin Dili | Türkçe |
Dersin Seviyesi | Doktora |
Dersin Türü | Seçmeli |
Dersin Koordinatörü | Prof.Dr. MAHMUT AKYİĞİT |
Dersi Verenler | |
Dersin Yardımcıları | |
Dersin Kategorisi | Diğer |
Dersin Amacı | 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 |
Dersin İçeriği | 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 |
# | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
---|---|---|---|
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, |
Hafta | Ders Konuları | Ön Hazırlık |
---|---|---|
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 |
Kaynaklar | |
---|---|
Ders Notu | 1.) Daniel Huybrechts, Complex geometry, Springer, 1965. 2.) Kunihiko Kodaira, Complex manifold and deformation of complex structures, Springer, 1981. |
Ders Kaynakları |
Sıra | Program Çıktıları | Katkı Düzeyi | |||||
---|---|---|---|---|---|---|---|
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 |
Değerlendirme Sistemi | |
---|---|
Yarıyıl Çalışmaları | Katkı Oranı |
1. Ara Sınav | 70 |
1. Kısa Sınav | 10 |
1. Ödev | 10 |
2. Ödev | 10 |
Toplam | 100 |
1. Yıl İçinin Başarıya | 50 |
1. Final | 50 |
Toplam | 100 |
AKTS - İş Yükü Etkinlik | Sayı | Süre (Saat) | Toplam İş Yükü (Saat) |
---|---|---|---|
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 |
Toplam İş Yükü | 158 | ||
Toplam İş Yükü / 25 (Saat) | 6,32 | ||
Dersin AKTS Kredisi | 6 |