On the space of harmonic 2-spheres in \bf CP²

1995/10/06 by L. Lemaire, Luc Lemaire, J. C. Wood +3
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #dg-ga #math.DG

paper · pdf · doi:10.48550/arxiv.dg-ga/9510003

Minor revision to take into account improved result of T.A. Crawford. Abstract and p. 2 changed plus some typos corrected. 15 pages. Latex 2.09 To appear in Internat. J. Math

openalex publication_date 1995/10/06 · arxiv created 1996/03/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Carrying further work of T.A. Crawford, we show that each component of the space of harmonic maps from the 2-sphere to complex projective 2-space of degree d and energy 4 πE is a smooth closed submanifold of the space of all C^j maps (j ≥ 2). We achieve this by showing that the Gauss transform which relates them to spaces of holomorphic maps of given degree and ramification index is \bf smooth and has \bf injective differential.

Related

• The Space of Harmonic Maps from the 2-sphere to the Complex Projective Plane
• Jacobi fields along harmonic 2-spheres in \bf CP² are integrable
• Harmonic Gauss maps of submanifolds of arbitrary codimension of the Euclidean space and sphere and some applications
• A note on the spectral deformation of harmonic maps from the two-sphere into the unitary group
• Spaces of harmonic maps of the projective plane to the four-dimensional sphere