HORIZONTAL LIFTS IN A SEMI-TENSOR BUNDLE DEFINED BY PROJECTION OF THE COTANGENT BUNDLE BUNDLE


Thesis Type: Postgraduate

Institution Of The Thesis: Ataturk University, Fen Bilimleri Enstitüsü, Matematik Anabilim Dalı, Turkey

Approval Date: 2021

Thesis Language: Turkish

Student: Merve Gamze MAVİYILDIZ

Supervisor: Furkan Yıldırım

Abstract:

In this thesis, using projection of the cotangent bundle T*M over a manifold M, we define a semi-tensor bundle tM of type (p,q). The aim of the study is to investigate horizontal lifts of vector fields in special class of semi-tensor bundle tM of type (p,q). Furthermore, we investigate some lifts of tensor fields of type (1,0) on a cross-section in the semi-tensor (pullback) bundle tM of tensor bundle TM of type (p,q) by using projection (submersion) of the cotangent bundle T*M and we find some geometric relations for them.