Biharmonic submanifolds of generalized space forms. (English) Zbl 1355.53053
Summary: We consider biharmonic submanifolds in both generalized complex and Sasakian space forms. After giving the biharmonicity conditions for submanifolds in these spaces, we study different particular cases for which we obtain curvature estimates. We consider curves, complex and Lagrangian surfaces and hypersurfaces for the generalized complex space form as well as hypersurfaces, invariant and anti-invariant submanifolds in the case of generalized Sasakian space forms.
MSC:
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
| 53C43 | Differential geometric aspects of harmonic maps |
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