Surfaces with flat normal connection in 4-dimensional space forms

2025/01/27 by Naoya Ando, Ando, Naoya, Ryusei Hatanaka +1 · 2 citations
Engineering · Mathematics · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Geometric Analysis and Curvature Flows #Material Science and Thermodynamics

paper · pdf · doi:10.48550/arxiv.2501.15780

Abstract

Let N be a Riemannian, Lorentzian or neutral 4-dimensional space form with constant sectional curvature L₀. 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≡ L₀ 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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• The twistor lifts of surfaces in 4-spaces
• The equations of Gauss, Codazzi and Ricci of surfaces in 4-dimensional space forms

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