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