On spectral geometry of minimal surfaces in 𝐂𝐏ⁿ

Shen, Yi Bing

doi:10.1090/S0002-9947-1995-1308022-6

On spectral geometry of minimal surfaces in $\mathbf {C}\mathrm {P}^ n$
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Trans. Amer. Math. Soc. 347 (1995), 3873-3889 Request permission

Abstract:

By employing the standard isometric imbedding of $C{P^n}$ into the Euclidean space, a classification theorem for full, minimal, $2$-type surfaces in $C{P^n}$ that are not $\pm$ holomorphic is given. All such compact minimal surfaces are either totally real minimal surfaces in $C{P^2}$ or totally real superminimal surfaces in $C{P^3}$ and $C{P^4}$. In the latter case, they are locally unique. Moreover, some eigenvalue inequalities for compact minimal surfaces of $C{P^n}$ with constant Kaehler angle are shown.

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