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Lagrangian submanifolds of the three dimensional complex projective space. (English) Zbl 1009.53056

This paper centers on the description of two types of Lagrangian submanifolds of \(\mathbb{C}\mathbb{P}^3\). These special Lagrangian submanifolds are defined in terms of particular qualities of orthonormal tangent frames on them. This involves various coefficients which arise in the frame descriptions of, for instance, covariant derivatives. The authors prove the existence of their types of Lagrangian submanifolds in certain cases and, under assumptions on the coefficients mentioned above, also prove several classification results.

MSC:

53D12 Lagrangian submanifolds; Maslov index
53B25 Local submanifolds
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