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 -