What question did this study set out to answer?

To establish necessary conditions and classification theorems for space-like and time-like surfaces with positive relative nullity in Robertson-Walker space-times.

April 1, 2026Open Access

Surfaces in Robertson-Walker Space-Times with Positive Relative Nullity

Key Points

To establish necessary conditions and classification theorems for space-like and time-like surfaces with positive relative nullity in Robertson-Walker space-times.
Characterization of space-like and time-like surfaces in L4_1(f,c)
Establish conditions for positive relative nullity
Derive local classification theorems for surfaces in L4_1(f,0)
Examine surfaces in E^1_1 x S^3 and E^1_1 x H^3
Found necessary and sufficient conditions for surfaces in L4_1(f,c)
Obtained local classification theorems that classify surfaces effectively
Identified special cases for constant warping functions leading to positive relative nullity

Abstract

Abstract In this article, we study space-like and time-like surfaces in a Robertson-Walker space-time, denoted by L⁴₁ (f, c) L 1 4 (f, c), having positive relative nullity. First, we give the necessary and sufficient conditions for such space-like and time-like surfaces in L⁴₁ (f, c) L 1 4 (f, c). Then, we obtain the local classification theorems for space-like and time-like surfaces in L⁴₁ (f, 0) L 1 4 (f, 0) with positive relative nullity, where the second factor is 3-dimensional Euclidean space. Finally, we consider the space-like and time-like surfaces in E¹₁ S³ E 1 1 × S 3 and E¹₁ H³ E 1 1 × H 3 with positive relative nullity. These are the special spaces of L⁴₁ (f, c) L 1 4 (f, c) when the warping function f is a constant function, with c=1 c = 1 for E¹₁ S³ E 1 1 × S 3 and c=-1 c = - 1 for E¹₁ H³ E 1 1 ×</mml:

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