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arXiv · 2505.13874

The equations of Gauss, Codazzi and Ricci of surfaces in 4-dimensional space forms

Naoya Ando
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Abstract

Let $N$ be a Riemannian, neutral or Lorentzian $4$-dimensional space form. In this paper, the expressions of the equations of Gauss, Codazzi and Ricci of a space-like or time-like surface in $N$ given in [7] are naturally understood in terms of the induced connection (of the complexification) of the two-fold exterior power of the pull-back bundle on the surface. Moreover, based on such expressions, we characterize several classes of surfaces related to the covariant derivatives of the twistor lifts and so on.

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Naoya Ando. 2025-05-20. The equations of Gauss, Codazzi and Ricci of surfaces in 4-dimensional space forms. https://arxiv.org/abs/2505.13874

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