Ordu University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
FMA657	TENSOR BUNDLES AND FIBERS I	Compulsory	1	1	6

Level of Course Unit

Second Cycle

Objectives of the Course

• to give tensor bundle of manifold andto get lifts of base manifold objects in this bundle.

Name of Lecturer(s)

Yrd. Doç. Dr. Seher ASLANCI

Learning Outcomes

1	To make types of tensor bundles of the manifold
2	To make fibers of geometric objects of manifolds to Tensor bundles
3	To make expansion of Structures on manifolds (almost complex, almost product and others) in tensor bundle

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

• Tangent Bundle • Vertical fibers • Full fiber • Fiber of Diversion • Fiber of Afinor • Full fiber of Affine connection • Formulas on Lie derivative • Horizontal fibers • Horizontal fiber of vector fields • The horizontal fibers of tensor fields • Horizontal fiber of affine connection • The horizontal fiber of Lie derivative

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	(1,0)-type tensor bundle (tangent bundle)
2	Vertical and complete lifts of functions
3	The vertical, horizontal and complete lifts of Vector fields
4	Vertical, Horizontal, and full lifts of Covector fields
5	Full lift of connection
6	Lift of Diversion, the connection with its vector fields lift
7	Full and horizontal Lift of Afinor structure
8	Midterm exam
9	Full and Horizontal Lift of tensor field
10	The Formulas of Lie derivative
11	Geodesics Lifts
12	Almost Complex Structure Lifts
13	AboutlLifts of Riemannian manifold in tangent bundle
14	Cross-sections of bundle and Lift Problems
15	Selected roofs (adapted) in bundle and lifts expressions in this roofs
16	Final exam

Recommended or Required Reading

1.Yano, K., Ishihara Sh. Tangent and cotangent bundles. Differential Geometry, Marsel Dekker, Inc, New York, 1973 2.L. A. Cordero, C. T. J. Dodson and M. De Leon, Differential Geometry of Frame bundles, Matematics and its Applications, 47, Kluwer Academic Publishers Group, Dordrecht, 1989

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
SUM		0
End Of Term (or Year) Learning Activities	Quantity	Weight
SUM		0
Yarıyıl (Yıl) İçi Etkinlikleri		40
Yarıyıl (Yıl) Sonu Etkinlikleri		60
SUM		100

Language of Instruction

Turkish

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	2	2
Final Examination	1	2	2
Makeup Examination	1	2	2
Attending Lectures	14	3	42
Self Study	14	9	126
Individual Study for Homework Problems	10	4	40
Individual Study for Mid term Examination	1	10	10
Individual Study for Final Examination	1	20	20
TOTAL WORKLOAD (hours)			244

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7
LO1
LO2
LO3

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High