Lifts of Structures on Product Manifolds

TL;DR

This paper extends the theory of lifting geometric structures to higher orders on product manifolds, building on previous work on complex manifolds and their k-th order extensions.

Contribution

It introduces the concept of k-th extended spaces of product manifolds and defines various higher order lifts of geometric structures on these manifolds.

Findings

Defined k-th extended spaces for product manifolds

Presented higher order vertical, complete, complete-vertical, and horizontal lifts

Extended the framework of structure lifting to more complex manifold constructions

Abstract

This article presents the further steps of the previously done studies taking into consideration the k-th order extensions of a complex manifold. In the previous studies higher order vertical and complete lifts of structures on the complex manifold were introduced. Presently, k-th extended spaces of a product manifold have been set and the higher order vertical, complete, complete- vertical and horizontal lifts of geometric structures on the product manifold have been presented.