Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
COMPLEX MANİFOLDS II MAT 628 0 3 + 0 3 6
 Dersin Dili Türkçe Dersin Seviyesi Doktora Dersin Türü SECMELI Dersin Koordinatörü Doç.Dr. MAHMUT AKYİĞİT Dersi Verenler Dersin Yardımcıları Dersin Kategorisi 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
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/she learns hermit manifolds 1 - 2 - 3 - 10 - 14 - 15 - A - C - 2 - He/she realizes Kahler metric and solves its examples 1 - 2 - 3 - 10 - 14 - 15 - A - C - 3 - He/she realizes cuvatures tensors of kahler manifolds 1 - 2 - 3 - 10 - 14 - 15 - A - C - 4 - He/she defines and compares submanifolds of kahler manifolds 1 - 2 - 3 - 10 - 14 - 15 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 10:Brain Storming 14:Self Study 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
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

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
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

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
KisaSinav 1 10
Odev 1 10
Odev 2 10
Toplam 100
Yıliçinin Başarıya Oranı 50
Finalin Başarıya Oranı 50
Toplam 100

#### AKTS - İş Yükü

Etkinlik Sayısı Süresi(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(s) 6.32
Dersin AKTS Kredisi 6.32
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