Problems of Lifts in Symplectic Geometry

VB-structures and generalizations

“…There is a huge list of various concepts of lifting tensor fields and other geometric structures from M to Ì r M (e.g. [13,25,30,42,48,60,61,62,65,69,79]), starting from the complete tangent lifts [33,34,39,46,47,64,75,76,77,78,80]. We will use mainly [63] and [48], where the descriptions of lifts (prolongations) are the same although based on different concepts.…”

Novel theorems for the cotangent bundle endowed with metallic structures on a differentiable manifold

“…They have explored the lifts of the tensor fields and connections on any manifold M to its cotangent manifold TM . Solimov et al have investigated almost complex structures in TM [25] , [26] , [27] . Gezer and Salimov [8] have studied diagonal lifts of tensor fields of type (1,1) on cross-sections in tensor bundles.…”

Metallic Structures for Tangent Bundles over Almost Quadratic ϕ-Manifolds

“…Tanno [10] studied complete and vertical lifts of an almost contact structure on TM and defined a tensor field J of type (1,1) and proved that it is an almost complex structure on TM. Numerous investigators have studied various geometric structures on TM-an almost complex structure by Yano [11], paracomplex structures by Tekkoyun [12], almost r-contact structures by Das and Khan [13], and many others [14][15][16][17][18][19].…”

“…In [20], Azami explored complete and horizontal lifts of metallic structures and analyzed the geometric properties of these structures. Salimov et al [19] studied complete lifts of symplectic vector fields on tangent and cotangent bundles. Recently, Khan [21] introduced a new tensor field J of type (1,1) and demonstrated that J is a metallic structure (MS) on the frame bundle FM.…”