The objective of this study was to investigate the behavior of relativistic G(QE) ${}_n$ string cloud spacetime endowed with various forms of the string cloud energy-momentum tensor $\mathcal{T}$, which includes the string cloud fluid density $\alpha$ and string tension $\beta$. A G(QE) ${}_n$ string cloud spacetime with a covariantly constant energy-momentum tensor satisfies the equation of state $\frac{\alpha }{\beta }=-1$, and represents either a massive string cloud spacetime or a bulk viscous fluid spacetime. Moreover, when a string cloud spacetime is coupled with a covariantly constant energy-momentum tensor, the equation of state $\frac{\alpha }{\beta }=-1$ coincides with the state equation for a cloud of geometric strings or represents the quintessence era. G(QE) ${}_n$ string cloud spacetimes with Codazzi-type and pseudo-symmetric energy-momentum tensors were investigated. Furthermore, we characterized $\mathcal{T}$-recurrent, weakly $\mathcal{T}$-symmetric, specially weakly $\mathcal{T}$-symmetric, generalized $\mathcal{T}$-recurrent, semi-generalized $\mathcal{T}$-recurrent, and quadratic Killing-type energy-momentum tensors on a string cloud spacetime with a Killing velocity vector field, and concluded that the string cloud spacetime either represents a massive string cloud spacetime or corresponds to the quintessence era.

This work studies the complete lifts of Kenmotsu manifolds associated with the generalized Tanaka-Webster connection (GTWC) in the tangent bundle. Using the GTWC, this study explores the complete lifts of various curvature tensors and geometric structures from Kenmotsu manifolds to their tangent bundles. Specifically, it examines the complete lifts of Ricci semi-symmetry, the projective curvature tensor, $\mathrm{\Phi }$-projectively semi-symmetric structures, the conharmonic curvature tensor, the concircular curvature tensor, and the Weyl conformal curvature tensor. Additionally, the research delves into the complete lifts of Ricci solitons on Kenmotsu manifolds with the GTWC within the tangent bundle framework, providing new insights into their geometric properties and symmetries in the lifted space. The data on the complete lifts of the Ricci soliton in Kenmotsu manifolds associated with the GTWC in the tangent bundle are also investigated. An example of the complete lifts of a $5$-dimensional Kenmotsu manifold is also included.