Another View on the Shape Equation for Strings

TL;DR

This paper explores the geometric conditions under which an M-dimensional extended object, like a string, forms a zero mean curvature surface in higher-dimensional Minkowski space, contributing to understanding string shape equations.

Contribution

It provides a new perspective on the shape equation for strings, analyzing conditions for M-brane solutions in Minkowski space.

Findings

Derived conditions for M-brane solutions in Minkowski space.

Analyzed the shape equation for closed strings.

Connected string geometry with zero mean curvature surfaces.

Abstract

The question how an $M$-dimensional extended object must be shaped so that a rigid motion gives an $M$-brane solution ($M+1$ dimensional timelike zero mean curvature surface) in $M+2$ dimensional Minkowski space is discussed for closed strings