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We give the definition of -biminimal submanifolds and derive the equation for -biminimal submanifolds. As an application, we give some examples of -biminimal manifolds. Finally, we consider -minimal hypersurfaces in the product space and derive two rigidity theorems.
It is shown that Fueter regular functions appear in connection with the Eells condition for harmonicity. New conditions for mappings from 4-dimensional conformally flat manifolds to be harmonic are obtained.
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