Isometric deformations of the K^(1/4)-flow translators in R^3 with helicoidal symmetry

TL;DR

This paper characterizes all helicoidal K^(1/4)-flow translators in R^3 by explicitly describing their moduli space, linking geometric properties with solutions to the unimodular Hessian equation.

Contribution

It provides a complete geometric classification of helicoidal K^(1/4)-flow translators through explicit moduli space determination.

Findings

Explicit description of the moduli space of helicoidal translators

Connection between height functions and the unimodular Hessian equation

Geometric construction from planar curves

Abstract

The height functions of K^(1/4)-flow translators in Euclidean space R^3 solve the unimodular Hessian equation. We explicitly and geometrically determine the moduli space of all helicoidal K^(1/4)-flow translators, which are generated from planar curves by the action of helicoidal groups.