On a stack of surfaces obtained from the $\mathbb{C}{P}^{N-1}$ sigma models

Abstract

Under the assumption that the $\mathbb{C}{P}^{N-1}$ sigma model is defined on the Riemann sphere and its action functional is finite, we derive surfaces induced by surfaces and we demonstrate that the stacked surfaces coincide with each other, which means idempotency of the recurrent procedure. Along the path to the solutions of the $\mathbb{C}{P}^{N-1}$ model equations, we demonstrate that the Euler--Lagrange equations for the projectors admit larger classes of solutions than the ones corresponding to rank-1 projectors.

12 pages, no figures

References in corpus (5)

• Invariant recurrence relations for CP^(N-1) models
• The geometric Cauchy problem for the membrane shape equation
• Description of surfaces associated with $C{P}^{N-1}$ sigma models on Minkowski space
• On the surfaces associated with $\mathbb{C}{P}^{N-1}$ models
• Soliton surfaces associated with sigma models; differential and algebraic aspect