Structures on the Manifolds and Bundles Lift Problems — Haşim Çayır

There are a lot of structures on bundles Tangent bundle Cotangent bundle Semi Cotangent bundle Tensor bundle etc and n dimensional differential manifolds Mn The integrability of tensorial structures on a manifold and their extension to bundles such as tangent and cotangent bundles has been an active research topic for the last 60 years Firstly Japanese mathematician S Sasaki 1912 1987 studies the differential geometry of tangent bundles of Riemannian manifolds in 1958 Later the subject of lift and bundle constantly improved Afterward Ishihara and Yano Ishihara and Yano 1973 obtained the integrability conditions of the F structure satisfying the condition of F3 F 0 By and by a lot of structures on the manifold and bundles studies by valuable authors Tachibana 1960 Norden 1960 Sato 1968 Shirokov 1966 Vishnevskii 1970 Kruchkovich 1972 Salimov 1994 Differential geometric applications of tensor operators are a very fruitful area of research in the modern study of differential geometry However despite its importance tensor operators structures and related issues are not well known yet In addition there are very few reference books in this field that can be referenced In this context all structures on Mn and bundles from the beginning to the present combined in this book We believe that this research book will provide a systematic description of tensor operators and structure theory and especially useful in master and doctoral education

There are a lot of structures on bundles Tangent bundle Cotangent bundle Semi Cotangent bundle Tensor bundle etc and n dimensional differential manifolds Mn The integrability of tensorial structures on a manifold and their extension to bundles such as tangent and cotangent bundles has been an active research topic for the last 60 years Firstly Japanese mathematician S Sasaki 1912 1987 studies the differential geometry of tangent bundles of Riemannian manifolds in 1958 Later the subject of lift and bundle constantly improved Afterward Ishihara and Yano Ishihara and Yano 1973 obtained the integrability conditions of the F structure satisfying the condition of F3 F 0 By and by a lot of structures on the manifold and bundles studies by valuable authors Tachibana 1960 Norden 1960 Sato 1968 Shirokov 1966 Vishnevskii 1970 Kruchkovich 1972 Salimov 1994 Differential geometric applications of tensor operators are a very fruitful area of research in the modern study of differential geometry However despite its importance tensor operators structures and related issues are not well known yet In addition there are very few reference books in this field that can be referenced In this context all structures on Mn and bundles from the beginning to the present combined in this book We believe that this research book will provide a systematic description of tensor operators and structure theory and especially useful in master and doctoral education