On conformal biharmonic immersions |
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Authors: | Ye-Lin Ou |
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Institution: | (1) Department of Mathematics, Texas A&M University—Commerce, Commerce, TX 75429, USA |
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Abstract: | This paper studies conformal biharmonic immersions. We first study the transformations of Jacobi operator and the bitension
field under conformal change of metrics. We then obtain an invariant equation for a conformal biharmonic immersion of a surface
into Euclidean 3-space. As applications, we construct a two-parameter family of non-minimal conformal biharmonic immersions
of cylinder into and some examples of conformal biharmonic immersions of four-dimensional Euclidean space into sphere and hyperbolic space,
thus providing many simple examples of proper biharmonic maps with rich geometric meanings. These suggest that there are abundant
proper biharmonic maps in the family of conformal immersions. We also explore the relationship between biharmonicity and holomorphicity
of conformal immersions of surfaces.
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Keywords: | Biharmonic maps Conformal biharmonic immersions Biharmonic submanifolds Jacobi operator |
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