On Pull-Back Bundle of Tensor Bundles Defined by Projection of The Cotangent Bundle

Using projection (submersion) of the cotangent bundle T*M over a manifold M, we define a semi-tensor (pull-back) bundle tM of type (p,q). The aim of this study is to investigate complete lift of vector fields in a special class of semi-tensor bundle tM of the type (p,q). We also have a new example for good square in this work.

THE HOMOGENEOUS LIFT TO THE (1, 1)-TENSOR BUNDLE OF A RIEMANNIAN METRIC

By using a Riemannian metric on a differentiable manifold, the homogeneous lift metric is introduced on the (1, 1)-tensor bundle of the Riemannian manifold. Some geometric objects related to this metric, such as the Levi-Civita connection, Riemannian curvature tensor and sectional curvature are calculated. Also, a para-Nordenian structure on the (1, 1)-tensor bundle with this metric is constructed and interesting properties of this structure are studied.