Surfaces with flat normal connection in 4-dimensional space forms

Naoya Ando; Ryusei Hatanaka

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arXiv · 2501.15780

Surfaces with flat normal connection in 4-dimensional space forms

Naoya Ando·Ryusei Hatanaka

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Abstract

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.

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Naoya Ando, Ryusei Hatanaka. 2025-01-27. Surfaces with flat normal connection in 4-dimensional space forms. https://arxiv.org/abs/2501.15780

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