Minimal surfaces with the Ricci condition in 4-dimensional space forms

Sakaki, Makoto

doi:10.1090/S0002-9939-1994-1195731-X

Minimal surfaces with the Ricci condition in $4$-dimensional space forms
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by Makoto Sakaki

Proc. Amer. Math. Soc. 121 (1994), 573-577

DOI: https://doi.org/10.1090/S0002-9939-1994-1195731-X

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Abstract:

Let ${X^N}(c)$ denote the N-dimensional simply connected space form of constant curvature c. We consider a problem to classify those minimal surfaces in ${X^N}(c)$ which are locally isometric to minimal surfaces in ${X^3}(c)$. In this paper we solve this problem in the case where $N = 4$, and give a result also in higher codimensional cases.

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