This article analyzes positive relative nullity in space-like and time-like surfaces, suggesting key theoretical classifications.
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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Demirci et al. (2026) studied this question.
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