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Keywords:
variational vector field; hypersurface; $f$-biminimal submanifold; mean curvature vector
variational vector field; hypersurface; $f$-biminimal submanifold; mean curvature vector
Summary:
We give the definition of $f$-biminimal submanifolds and derive the equation for $f$-biminimal submanifolds. As an application, we give some examples of $f$-biminimal manifolds. Finally, we consider $f$-minimal hypersurfaces in the product space $\mathbb {R}^{n}\times \mathbb {S}^{1}(a)$ and derive two rigidity theorems.
References:
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