GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION

SEMI-RIEMANNIAN GEOMETRY/4350218

COURSE INFO

-- LANGUAGE OF INSTRUCTION

Turkish

-- NAME OF LECTURER(S)

Assoc.Prof. Hasan ES

-- WEB SITE(S) OF LECTURER(S)

http://www.websitem.gazi.edu.tr/site/hasanes

-- EMAIL(S) OF LECTURER(S)

hasanes@gazi.edu.tr

-- LEARNING OUTCOMES OF THE COURSE UNIT

To gain skills for relation analysis and learning about this lecture.

-- MODE OF DELIVERY

The mode of delivery of this course is Face to face

-- PREREQUISITES AND CO-REQUISITES

There is no prerequisite or co-requisite for this course.

-- RECOMMENDED OPTIONAL PROGRAMME COMPONENTS

There is no recommended optional programme component for this course

--COURSE CONTENT
1. Week	Semi-Riemannian submanifolds. Tangent and normals.
2. Week	The induced connection. Geodesics in submanifolds.
3. Week	Totally Geodesic submanifolds. Semi-Riemannian hypersurfaces.
4. Week	Hyperquadrics. The Codazzi Equation. Totally umbilic hypersurfaces.
5. Week	The normal connection. Isometric immersions.
6. Week	Two-parameter maps. The Gauss lemma.
7. Week	Convex open sets. Arc length. Riemannian distance.
8. Week	Mid-term exam
9. Week	Riemannian completeness. Lorentz causal character.
10. Week	Timecones. Local Lorentz geometry.
11. Week	Geodesics in hyperquadrics,Geodesics in surfaces.
12. Week	Orientability. Semi-Riemannian Coverings.
13. Week	Lorentz time-orientability. Volume elements.
14. Week	Jacobi fields. Locally symmetric manifolds.
15. Week	Semi-orthogonal groups. Some isometry groups.
16. Week	Final Exam

-- RECOMMENDED OR REQUIRED READING

Semi-Riemannian Geometry with Application to Relativity, Barret O’Neill

-- PLANNED LEARNING ACTIVITIES AND TEACHING METHODS

Lecture, Question & Answer, Demonstration, Drill - Practise

-- WORK PLACEMENT(S)

-- ASSESSMENT METHODS AND CRITERIA

	Quantity	Percentage
Mid-terms	1	40
Assignment	0	0
Exercises	0	0
Projects	0	0
Practice	0	0
Quiz	0	0
Contribution of In-term Studies to Overall Grade		40
Contribution of Final Examination to Overall Grade		60

-- WORKLOAD

Efficiency	Total Week Count	Weekly Duration (in hour)	Total Workload in Semester
Theoretical Study Hours of Course Per Week	14	3	42
Practising Hours of Course Per Week			0
Reading	10	5	50
Searching in Internet and Library			0
Designing and Applying Materials			0
Preparing Reports	10	5	50
Preparing Presentation			0
Presentation			0
Mid-Term and Studying for Mid-Term	1	20	20
Final and Studying for Final	1	25	25
Other			0
TOTAL WORKLOAD:			187
TOTAL WORKLOAD / 25:			7.48
ECTS:			7.5

-- COURSE'S CONTRIBUTION TO PROGRAM

Gazi University