1. SECOND CYCLE - MASTER'S DEGREE
  2. THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES
  3. MATHEMATICS DEPARTMENT
  4. 1441 Mathematics
Course Information Course Learning Outcomes Course's Contribution To Program ECTS Workload Course Details
Print

COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 565SEMI-RIEMANN MANIFOLDS II3 + 02nd Semester7,5

COURSE DESCRIPTION
Course Level Master's Degree
Course Type Elective
Course Objective Study of different geometric structures of Riemann surfaces and the semi-Riemannian.
Course Content Tangents and Normals, Reduced Connections, Geodesic Submanifolds, Semi-Riemann Hypersurfaces, Hyperquadrics, Codazzi Equation, Total Umbilical Hypersurfaces, Normal Connections, Congruent Theorem, Isometric Immertions, Mappings with Two Parameters.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.

COURSE LEARNING OUTCOMES
1Knows the Tangents and Normals, Identifies the Reduced Connections, Geodesic Submanifolds.
2Learns the Semi-Riemann Hypersurfaces, Hyperquadrics, Codazzi Equation.
3Learns the Total Umbilical Hypersurfaces, Normal Connections, Congruent Theorem.
4Identifies the Isometric Immertions, Mappings with Two Parameters.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08
LO 0014 45   5
LO 0025 54   4
LO 0034  5   5
LO 0044 55  4 
Sub Total17 1419  414
Contribution40450014

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)14342
Hours for off-the-classroom study (Pre-study, practice)14798
Assignments155
Mid-terms11515
Final examination13535
Total Work Load

ECTS Credit of the Course





195

7,5
COURSE DETAILS
 Select Year   


 Course TermNoInstructors
Details 2012-2013 Spring1CANSEL AYCAN ÖZDEMİR


Print

Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester Mode of Delivery
MAT 565 SEMI-RIEMANN MANIFOLDS II 3 + 0 1 Turkish 2012-2013 Spring Face to Face
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. CANSEL AYCAN ÖZDEMİR c_aycan@pau.edu.tr FEN A0304 %70
Goals Study of different geometric structures of Riemann surfaces and the semi-Riemannian.
Content Tangents and Normals, Reduced Connections, Geodesic Submanifolds, Semi-Riemann Hypersurfaces, Hyperquadrics, Codazzi Equation, Total Umbilical Hypersurfaces, Normal Connections, Congruent Theorem, Isometric Immertions, Mappings with Two Parameters.
Topics
WeeksTopics
1 tangent vectors, vector fields, 1-forms
2 curves, differentiable maps
3 topologic and differentiable manifolds
4 immersions and submersions
5 submanifolds, some special manifolds
6 tensor fields, tensor algebra
7 isometries, levi-civita connections
8 middterm exam
9 geodesics, exponential maps
10 semi-riemann surfaces, semi-riemann manifolds
11 ricci and scalar curvature
12 semi-riemann product manifolds
13 semi-riemann hypersurfaces, semi-riemann submanifolds
14 final exam
Materials
Materials are not specified.
Resources
ResourcesResources Language
Semi-Riemann Geometry, B. O'NeillTürkçe
Course Assessment
Assesment MethodsPercentage (%)Assesment Methods Title
Final Exam50Final Exam
Midterm Exam50Midterm Exam
L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes