Application of the moving frame method to deformed Willmore surfaces in space forms

JOURNAL OF GEOMETRY AND PHYSICS

卷:128

Article

Paragoda, Thanuja¹ 

[1] Univ Sri Jayewardenepura, Fac Sci Appl, Dept Math, Nugegoda 10250, Sri Lanka

关键词: Deformed Willmore energy;    Space forms;    Moving frame;   

DOI  :  10.1016/j.geomphys.2018.02.010

来源: Elsevier

【 摘 要 】

The main goal of this paper is to use the theory of exterior differential forms in deriving variations of the deformed Willmore energy in space forms and study the minimizers of the deformed Willmore energy in space forms. We derive both first and second order variations of deformed Willmore energy in space forms explicitly using moving frame method. We prove that the second order variation of deformed Willmore energy depends on the intrinsic Laplace Beltrami operator, the sectional curvature and some special operators along with mean and Gauss curvatures of the surface embedded in space forms, while the first order variation depends on the extrinsic Laplace Beltrami operator. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free