Biconservative Surfaces in Robertson-Walker Spaces

TL;DR

This paper investigates space-like biconservative surfaces in Robertson-Walker spacetimes, deriving geometric properties and classifying such surfaces in specific dimensions, revealing their embedding in totally geodesic submanifolds.

Contribution

It provides the first complete local classifications of space-like biconservative surfaces in certain Robertson-Walker spaces and establishes their embedding properties.

Findings

Complete local classifications in $L^4_1(f,0)$, $L^5_1(f,0)$, and $L^5_1(1, ext{±}1)$.

Geometric properties of biconservative surfaces in arbitrary dimensions.

Space-like PMCV biconservative surfaces lie on totally geodesic submanifolds of dimension 4 or 5.

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 $L^n_1(f, c)$ of arbitrary dimension. Then, we get complete local classifications of such surfaces in $L^4_1(f,0)$, $L^5_1(f,0)$ and $L^5_1(1,\pm 1)$. Finally, we proved that a space-like PMCV biconservative surface in $L^n_1(f,0)$ lies on a totally geodesic submanifold with dimension $4$ or $5$.