what do they call the style of dancing that is performed on suspended ropes or sheets similar to pole dancing?

Answer 1

Unless you're talking about some other form of erotic dancing (which is what pole dancing is), then I think you're looking for the term "aerial dance."

Check out this article, "Aerial dance sweeps the nation."
http://www.usatoday.com/life/2001-07-25-aerial-dance.htm

Answer 2

is this what your talking about?
A Spanish web is a contortion act that is performed high above the stage while holding on to a loop in a thick soft rope that is hung from the roof.

heres a video of a spanish web act
http://youtube.com/watch?v=FvWq90u9AsE

Answer 3

suspended rope dancing