On space‐like class A$\mathcal {A}$ surfaces in Robertson–Walker spacetimes

Burcu Bektaş Demirci, Nurettin Cenk Turgay and Rüya Yeğin Şen

Mathematische Nachrichten, 2025, vol. 298, issue 2, 718-729

Abstract: In this paper, we consider space‐like surfaces in Robertson–Walker spacetimes L14(f,c)$L^4_1(f,c)$ with the comoving observer field ∂∂t$\frac{\partial }{\partial t}$. We study some problems related to such surfaces satisfying the geometric conditions imposed on the tangential and normal parts of the unit vector field ∂∂t$\frac{\partial }{\partial t}$, as naturally defined. First, we investigate space‐like surfaces in L14(f,c)$L^4_1(f,c)$ satisfying that the tangent component of ∂∂t$\frac{\partial }{\partial t}$ is an eigenvector of all shape operators, called class A$\mathcal {A}$ surfaces. Then, we get a classification theorem for space‐like class A$\mathcal {A}$ surfaces in L14(f,0)$L^4_1(f,0)$. Also, we examine minimal space‐like class A$\mathcal {A}$ surfaces in L14(f,0)$L^4_1(f,0)$. Finally, we give the parameterizations of space‐like surfaces in L14(f,0)$L^4_1(f,0)$ when the normal part of the unit vector field ∂∂t$\frac{\partial }{\partial t}$ is parallel.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202400374

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:298:y:2025:i:2:p:718-729

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().