Translation invariant surfaces in the 3-dimensional Heisenberg‎ ‎group

Document Type : Research Paper


1 Gyeongsang National University

2 University of Missouri-Columbia


‎In this paper‎, ‎we study translation invariant surfaces in the‎
‎3-dimensional Heisenberg group $rm Nil_3$‎. ‎In particular‎, ‎we‎
‎completely classify translation invariant surfaces in $rm Nil_3$‎
‎whose position vector $x$ satisfies the equation $Delta x = Ax$‎,
‎where $Delta$ is the Laplacian operator of the surface and $A$‎
‎is a $3 times 3$-real matrix‎.


Main Subjects

Volume 40, Issue 6 - Serial Number 6
December 2014
Pages 1373-1385
  • Receive Date: 02 April 2013
  • Revise Date: 08 October 2013
  • Accept Date: 08 October 2013
  • First Publish Date: 01 December 2014