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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.15780 |
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Table of Contents:
- Let $N$ be a Riemannian, Lorentzian or neutral $4$-dimensional space form with constant sectional curvature $L_0$. In this paper, noticing the linearly dependent condition, we obtain characterizations of space-like surfaces in $N$ with flat normal connection and parallel normal vector fields. In addition, we obtain a generic characterization of space-like surfaces in $N$ with flat normal connection and $K\equiv L_0$ which do not admit any parallel normal vector fields. For time-like surfaces in $N$ with flat normal connection, we obtain analogous results.