Geometric aspects of Bäcklund transformations of Weingarten submanifolds

Abstract

If /i and fi are immersions of an n-manifold M into R 2n-1 such that their induced frame bundles differ by a constant right action, then /i and fa both satisfy a Weingarten condition on their normal bundles and the right action corresponds to a generalization of the classical Backlund transformation.

TimelikeW-Surfaces in Minkowski 3-Spaceℝ13and the Sinh-Gordon Equation

“…Here, D and S are the usual flat connection on ℝ 3 1 , and shape operator on TðMÞ, respectively. The first equation of (9) gives…”

“…In 1990, Palmer constructed Backlund's transformation between spacelike and timelike surfaces of constant negative curvature in ℝ 3 1 [8]. At that decade, some researchers gave Backlund's transformations on Weingarten surfaces [8][9][10][11]. The second author presented the Minkowski versions of the Backlund theorem and its application by using the method of moving frames [12].…”

Motions of Curves in the Pseudo-Galilean SpaceG31

“…In 1990 Palmer constructed a Backlund transformation between spacelike and timelike surfaces of constant negative curvature in E 3 1 [5]. At that decade some researchers gave Backlund transformations on Weingarten surfaces [6][7][8][9].…”