Mixed doubly sequential warped product manifolds

Abstract This research aims to expand the understanding of solutions to Einstein’s field equations by introducing a new class of warped product manifolds, specifically mixed doubly sequential manifolds. The study delves into the geometry of these manifolds by analyzing critical metrics, including curvature tensors, covariant derivatives, and Ricci curvature. It also explores the properties of geodesics and conformal vector fields and the Hessian and concircular tensors on the sequential warped product manifold. Key findings include detailed formulations of curvature properties and the conditions under which these manifolds exhibit Einstein characteristics. The study provides comprehensive definitions and insights that facilitate the application of mixed doubly sequential warped product manifolds in further research. The introduction of mixed doubly sequential warped product manifolds presents significant implications for both mathematics and physics, particularly in constructing solutions to Einstein’s equations.