TY - JOUR

T1 - Generalized polar transforms of spacelike isothermic surfaces

AU - Wang, Peng

N1 - Funding Information:
The author is grateful to Professor Xiang Ma for valuable discussions and suggestions. The author’s work was supported by Program for Young Excellent Talents in Tongji University and the Tianyuan Foundation of China , grant 10926112 .

PY - 2012/2

Y1 - 2012/2

N2 - In this paper, we generalize the polar transforms of spacelike isothermic surfaces in Q14 to n-dimensional pseudo-Riemannian space forms Qrn. We show that there exist c-polar spacelike isothermic surfaces derived from a spacelike isothermic surface in Qrn, which are into Srn+1(c), Hr-1n+1(c) or Qrn 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.

AB - In this paper, we generalize the polar transforms of spacelike isothermic surfaces in Q14 to n-dimensional pseudo-Riemannian space forms Qrn. We show that there exist c-polar spacelike isothermic surfaces derived from a spacelike isothermic surface in Qrn, which are into Srn+1(c), Hr-1n+1(c) or Qrn 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.

KW - Christoffel transform

KW - Darboux transform

KW - Permutability theorem

KW - Spacelike isothermic surfaces

KW - Spectral transform

KW - c-polar transform

UR - http://www.scopus.com/inward/record.url?scp=82055184031&partnerID=8YFLogxK

U2 - 10.1016/j.geomphys.2011.11.003

DO - 10.1016/j.geomphys.2011.11.003

M3 - Article

AN - SCOPUS:82055184031

SN - 0393-0440

VL - 62

SP - 403

EP - 411

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

IS - 2

ER -