Geodesic incompleteness in the CP^1 model on a compact Riemann surface

Abstract

It is proved that the moduli space of static solutions of the CP^1 model on spacetime Sigma x R, where Sigma is any compact Riemann surface, is geodesically incomplete with respect to the metric induced by the kinetic energy functional. The geodesic approximation predicts, therefore, that lumps can collapse and form singularities in finite time in these models.

5 pages, Latex, no figures

Cited by in corpus (6)

• Integrable Chiral Theories in 2+1 Dimensions
• Dynamics of CP^1 lumps on a cylinder
• The volume of the space of holomorphic maps from S^2 to CP^k
• Gravity thaws the frozen moduli of the CP^1 lump
• The geodesic approximation for lump dynamics and coercivity of the Hessian for harmonic maps
• Ricci magnetic geodesic motion of vortices and lumps