Generalized polar transforms of spacelike isothermic surfaces

JOURNAL OF GEOMETRY AND PHYSICS

卷:62

Article

Wang, Peng

关键词: Spacelike isothermic surfaces;    c-polar transform;    Christoffel transform;    Darboux transform;    Spectral transform;    Permutability theorem;   

DOI  :  10.1016/j.geomphys.2011.11.003

来源: Elsevier

【 摘 要 】

In this paper, we generalize the polar transforms of spacelike isothermic surfaces in Q(1)(4) to n-dimensional pseudo-Riemannian space forms Q(r)(n). We show that there exist c-polar spacelike isothermic surfaces derived from a spacelike isothermic surface in Q(r)(n), which are into S-r(n+1)(c), H-r-1(n+1)(c) or Q(r)(n) depending on c > 0, < 0, or = 0. The c-polar isothermic surfaces can be characterized as generalized H-surfaces with null minimal sections. We also prove that if both the original surface and its c-polar surface are closed immersion, then they have the same Willmore functional. As examples, we discuss some product surfaces and compute the c-polar transforms of them. In the end, we derive the permutability theorems for c-polar transforms and Darboux transform and spectral transform of isothermic surfaces. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free