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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 564SEMI-RIEMANN MANIFOLDS I3 + 01st Semester7,5

COURSE DESCRIPTION
Course Level Master's Degree
Course Type Elective
Course Objective Teaching the basic concepts of Minkowski space and Lorentzian structures.
Course Content Symetric Bilinear Forms, Scalar Products, Isometries, Levi-Civita Connection, Parallel Translation, Geodesics, Exponential Mapping, Curvature, Cross Sectional Curvature, Semi-Riemann Surfaces, Type Change and Metric Contraction, Frame Fields, Some Differential Operators, Semi-Riemann Product Manifolds with Ricci ve Scalar Curvature, Local Isometries.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.
Mode of Delivery Face to Face

COURSE LEARNING OUTCOMES
1Realizes the Symetric Bilinear Forms, Scalar Products, Isometries.
2Identifies the Levi-Civita Connection, Parallel Translation, Geodesics, Exponential Mapping.
3Learns the Curvature, Cross Sectional Curvature, Semi-Riemann Surfaces, Type Change and Metric Contraction, Frame Fields.
4Identifies the Some Differential Operators, Semi-Riemann Product Manifolds with Ricci ve Scalar Curvature, Local Isometries.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08
LO 0014 55  4 
LO 0025 44   5
LO 0034 54  4 
LO 0045 45   4
Sub Total18 1818  89
Contribution50550022

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 2011-2012 Fall1CANSEL AYCAN
Details 2010-2011 Fall1CANSEL AYCAN


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester
MAT 564 SEMI-RIEMANN MANIFOLDS I 3 + 0 1 Turkish 2011-2012 Fall
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. CANSEL AYCAN c_aycan@pau.edu.tr Course location is not specified. %
Goals Teaching the basic concepts of Minkowski space and Lorentzian structures.
Content Symetric Bilinear Forms, Scalar Products, Isometries, Levi-Civita Connection, Parallel Translation, Geodesics, Exponential Mapping, Curvature, Cross Sectional Curvature, Semi-Riemann Surfaces, Type Change and Metric Contraction, Frame Fields, Some Differential Operators, Semi-Riemann Product Manifolds with Ricci ve Scalar Curvature, Local Isometries.
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