NDLI: On conformal biharmonic immersions

Content Provider	Springer Nature Link
Author	Ou, Ye Lin
Copyright Year	2009
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 $${\mathbb{R}^3}$$ 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.
Ending Page	142
Page Count	10
Starting Page	133
File Format	PDF
ISSN	0232704X
e-ISSN	15729060
Journal	Annals of Global Analysis and Geometry
Issue Number	2
Volume Number	36
Language	English
Publisher	Springer Netherlands
Publisher Date	2009-01-10
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geometry Biharmonic maps Statistics for Business/Economics/Mathematical Finance/Insurance Jacobi operator Mathematical and Computational Physics Analysis Harmonic maps etc. Conformal biharmonic immersions Group Theory and Generalizations Biharmonic submanifolds
Content Type	Text
Resource Type	Article
Subject	Analysis Geometry and Topology

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