Pseudo-parallel Lagrangian submanifolds in complex space forms. (English) Zbl 1158.53057
Summary: We study pseudo-parallel Lagrangian submanifolds in a complex space form. We give several general properties of pseudo-parallel submanifolds. For the 2-dimensional case, we show that any minimal Lagrangian surface is pseudo-parallel. We also give examples of non-minimal pseudo-parallel Lagrangian surfaces. Here we prove a local classification of the pseudo-parallel Lagrangian surfaces. In particular, semi-parallel Lagrangian surfaces are totally geodesic or flat. Finally, we give examples of pseudo-parallel Lagrangian surfaces which are not semi-parallel.
Keywords:
Lagrangian submanifold; minimal submanifold; pseudo-parallel submanifold; Legendre curve; complex space formReferences:
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