Gok, MustafaKilic, ErolOzgur, Cihan2024-08-042024-08-0420210393-04401879-1662https://doi.org/10.1016/j.geomphys.2021.104346https://hdl.handle.net/11616/100141In this paper, we define and study two new structures on a differentiable manifold called by us an f((a,b)) (3, 2, 1)-structure and a framed f((a,b)) (3, 2, 1)-structure as a generalization of some geometric structures determined by polynomial structures, where a, b is an element of R and b not equal 0. At beginning, we present some examples regarding f((a,b)) (3, 2,1)-structures and establish their some fundamental properties. We also give a necessary condition for an f((a,b)) (3, 2,1)-structure to be an almost quadratic phi-structure. Later, it is shown that the existence of two semi-Riemannian metrics on differentiable manifolds admitting a framed f((a,b)) (3, 2, 1)-structure, i.e., framed f((a,b)) (3, 2, 1)-manifolds. In particular, a framed f((a,b)) ( 3, 2,1)-manifold endowed with the first semi-Riemannian metric mentioned above is called a framed metric f((a,b)) (3, 2, 1)-manifold. Finally, we construct some examples to illustrate the existence of framed metric f((a,b)) (3, 2, 1)-manifolds. (C) 2021 Elsevier B.V. All rights reserved.eninfo:eu-repo/semantics/closedAccessPolynomial structureMetallic pseudo-Riemannian structureAlmost quadratic phi-structureepsilon-framed metric structureArticle16910.1016/j.geomphys.2021.1043462-s2.0-85112822019Q2WOS:000697339000010Q2