Surfaces with flat normal connection in 4-dimensional space forms

Fuente: arXiv
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Autores principales: Ando, Naoya, Hatanaka, Ryusei
Formato: Preprint
Publicado: 2025
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author Ando, Naoya
Hatanaka, Ryusei
author_facet Ando, Naoya
Hatanaka, Ryusei
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.
format Preprint
id arxiv_https___arxiv_org_abs_2501_15780
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Surfaces with flat normal connection in 4-dimensional space forms
Ando, Naoya
Hatanaka, Ryusei
Differential Geometry
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.
title Surfaces with flat normal connection in 4-dimensional space forms
topic Differential Geometry
url https://arxiv.org/abs/2501.15780