Biconservative Surfaces in Robertson-Walker Spaces

Nurettin Cenk Turgay; Rüya Yeğin Şen

paper

Biconservative Surfaces in Robertson-Walker Spaces

arXiv:2409.00132

Abstract

In this paper, we mainly focus on space-like PMCV surfaces in Robertson-Walker spacetimes. First, we derive certain geometrical properties of biconservative surfaces in the Robertson-Walker space $L_{1}^{n} (f, c)$ of arbitrary dimension. Then, we get complete local classifications of such surfaces in $L_{1}^{4} (f, 0)$ , $L_{1}^{5} (f, 0)$ and $L_{1}^{5} (1, \pm 1)$ . Finally, we proved that a space-like PMCV biconservative surface in $L_{1}^{n} (f, 0)$ lies on a totally geodesic submanifold with dimension $4$ or $5$ .