2023/07/29 by Naoya Ando, Ando, Naoya · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2307.15965
openalex publication_date 2023/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a Lorentz surface and F:M→ N a time-like and conformal immersion of M into a 4-dimensional neutral space form N with zero mean curvature vector. We see that the curvature K of the induced metric on M by F is identically equal to the constant sectional curvature L0 of N if and only if the covariant derivatives of both of the time-like twistor lifts are zero or light-like. If K≡ L0, then the normal connection ∇⊥ of F is flat, while the converse is not necessarily true. We see that a holomorphic paracomplex quartic differential Q on M defined by F is zero or null if and only if the covariant derivative of at least one of the time-like twistor lifts is zero or light-like. In addition, we see that K is identically equal to L0 if and only if not only ∇⊥ is flat but also Q is zero or null.