Title

Some Classifications of Biharmonic Maps Between 2-Spheres

Author

Sheng Lu

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

Date of Award

Summer 2015

Abstract

The purpose of the thesis is to study biharmonic maps between 2-spheres with a focus on constructions of examples of biharmonic maps between spheres or from a sphere into a sphere with a conformal factor, and the classifications of certain family of biharmonic maps between spheres. We tried to classify some biharmonic maps between 2-spheres by considering some special classes of maps and by changing the metric in the domain or the target manifolds. Our study was partially motivated by the rich theory, examples, and interesting applications of harmonic maps between spheres or from a 2-sphere.In the thesis, we prove that the complex conjugate of a proper map between 2-spheres still be proper biharmonic; then we prove that there is no proper biharmonic map in a certain family of maps between 2-spheres; also, we study some properties of biharmonic maps between spheres with conformal factors.

Advisor

Ye-Lin Ou

Subject Categories

Mathematics | Physical Sciences and Mathematics

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