On Time-Like Class A Surfaces of a Warped Space-time with Lorentzian Fiber

2025/09/11 by Furkan Kaya, Kaya, Furkan, Nurettin Cenk Turgay +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Algebraic and Geometric Analysis #Differential Equations and Numerical Methods

paper · pdf · doi:10.48550/arxiv.2509.16220

Abstract

In this paper, we consider time-like surfaces in the static space-time given by the warped product \mathbb L³₁(c) _f× (I,dz²), where \mathbb L³₁(c) denotes the Lorentzian space form with the constant sectional curvature c∈\-1,0,1\. In particular, we study the surfaces with light-like ((∂)/(∂ z))^T. First, we construct a globally defined pseudo-orthonormal frame field on a surface satisfying this condition and deal with the invariants associated with this frame field. Then, we obtain a complete classification theorem for class~\mathcal A surfaces. Finally, we consider some applications of this theorem.

Citations

• Codimension two spacelike submanifolds into null hypersurfaces of generalized Robertson-Walker spacetimes
• Biconservative Surfaces in Robertson-Walker Spaces
• Special Standard Static Space-Times
• Local anisotropy in self-gravitating systems

Related

• On Space-like Class \mathcal A Surfaces in Robertson-Walker Space Times
• Null Sectional Curvatures of Warped Products
• Surfaces in Robertson-Walker Space-Times with Positive Relative Nullity
• Zero mean curvature surfaces in Lorentz-Minkowski 3-space which change type across a light-like line
• Timelike surfaces with harmonic inverse mean curvature