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Transactions of the American Mathematical Society

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On spectral geometry of minimal surfaces in $ \bold C{\rm P}\sp n$

Author: Yi Bing Shen
Journal: Trans. Amer. Math. Soc. 347 (1995), 3873-3889
MSC: Primary 53C42; Secondary 58G25
MathSciNet review: 1308022
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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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Keywords: Minimal surface, Kaehler angle, complex projective space, finite type submanifolds
Article copyright: © Copyright 1995 American Mathematical Society

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