Czechoslovak Mathematical Journal, first online, pp. 1-13


$f$-biminimal maps between Riemannian manifolds

Yan Zhao, Ximin Liu

Received July 10, 2017.   Published online July 11, 2019.

Abstract:  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.
Keywords:  variational vector field; hypersurface; $f$-biminimal submanifold; mean curvature vector
Classification MSC:  53B25, 53C40
DOI:  10.21136/CMJ.2019.0328-17

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Affiliations:   Yan Zhao (corresponding author), College of Science, Henan University of Technology, Zhengzhou, Henan 450001, P. R. China, e-mail: zy4012006@126.com; Ximin Liu School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China, e-mail: ximinliu@dlut.edu.cn


 
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