Three-dimensional $C_{12}$-manifolds

Abstract

The present paper is devoted to three-dimensional C 12 -manifolds (defined by D. Chinea and C. Gonzalez), which are never normal. We study their fundamental properties and give concrete examples. As an application, we study such structures on three-dimensional Lie groups.

Ricci Soliton in Deformed C12-Manifolds

“…A 3-dimensional C 12 manifold exhibits complete controllability, signifying the existence of a naturally derived global orthonormal basis denoted by {ξ, ψ, ϕψ}. Then, from Corollary (3.2) of [2] , along with (1.1) and (1.3)we have,…”

Lorentz ${C_{12}}$-manifolds

“…Recently, C 12 -manifolds have become a well-known and intensively studied subject of research in differential geometry. The recent works [1,2,3,4,5] provide a detailed overview of the results obtained in this framework.…”

Characterization of 3-dimensional almost contact metric structures

“…For the class C 12 which is integrable and never normal, recently some works have been published on this subject. For example, [1,2,3,9]. But, for the class C 9 which is neither normal nor integrable, unfortunately, there is no study on it yet.…”