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
FMA658	TENSOR BUNDLES AND FIBERS II	Compulsory	1	2	6

Level of Course Unit

Second Cycle

Objectives of the Course

Objectives of Course is giving the tensor bundle of a manifold and taking lifts of the objects of base manifolds on this bundle.

Name of Lecturer(s)

Yrd. Doç. dr Seher ASLANCI

Learning Outcomes

1	Can find the type of tensor bundle of a manifold.
2	Can find the extension of structures (almost complex, almost product and others) on manifolds to tensor bunle.
3	Can find the lifts of geometric objects of manifolds to tensor bundle.

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Tangent Bundle, Vertical lifts, Complete lifts, Lifts of Derivations, Lifts of Affinor, Complete lifts of Affine Connection, Formulaes of Lie Derivation, Horizontal lifts, Horizontal lifts of Vector Fields, Horizontal lifts of Tensor Fields, Horizontal lifts of Affine Connection, Horizontal lifts of Lie Derivation.

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Tensor Bundle of Type (1,0). (Tangent Bundle)
2	Vertical and complete lifts of Functions
3	Vertical , Horizontal and Complete lifts of Vector Fields
4	Vertical , Horizontal and Complete lifts of Covector Fields
5	Complete lifts of Connection
6	Lifts of Derivations and, its connections to lifts of Vector Fields
7	Horizontal and Complete lifts of Affinor Structure
8	Mid Term Exam
9	Complete and Horizontal lifts of Tensor Fields
10	Formulaes of Lie Derivation
11	Lifts of Geodesics
12	Lifts of Almost Complex Structure
13	About the Lifts of Tangent Bundle on a Riemannian Manifold
14	Cross-section of Bundles and problem of Lifts
15	Selected Frames on Bundle (adapted) and expressions of Lifts on this frame
16	Final exam

Recommended or Required Reading

1. Yano, K., Ishihara Sh. Tangent and cotangent bundles. Differential Geometry, Marsel Dekker, Inc, New York, 1973 Other Tutorial 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
Attending Lectures	14	3	42
Problem Solving	14	1	14
Self Study	14	6	84
Individual Study for Homework Problems	7	3	21
Individual Study for Mid term Examination	1	10	10
Individual Study for Final Examination	1	20	20
TOTAL WORKLOAD (hours)			195

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