Jacobi fields along harmonic 2-spheres in ${\bf C}P^2$ are integrable

Details Jacobi fields along harmonic 2-spheres in ${\bf C}P^2$ are integrable Jacobi fields along harmonic 2-spheres in ${\bf C}P^2$ are integrable

2001-04-24

arxiv.org/abs/math/0104220v2

Mathematics

Differential Geometry

Latex 2e, 24 pages

Scientific paper

We show that any Jacobi field along a harmonic map from the 2-sphere to the complex projective plane is integrable (i.e., is tangent to a smooth variation through harmonic maps). This provides one of the few known answers to this problem of integrability, which was raised in different contexts of geometry and analysis. It implies that the Jacobi fields form the tangent bundle to each component of the manifold of harmonic maps from $S^2$ to ${\bf C}P^2$ thus giving the nullity of any such harmonic map; it also has bearing on the behaviour of weakly harmonic $E$-minimizing maps from a 3-manifold to ${\bf C}P^2$ near a singularity and the structure of the singular set of such maps from any manifold to ${\bf C}P^2$.

Affiliated with

Also associated with

No associations

Rating

Jacobi fields along harmonic 2-spheres in ${\bf C}P^2$ are integrable does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Jacobi fields along harmonic 2-spheres in ${\bf C}P^2$ are integrable, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Jacobi fields along harmonic 2-spheres in ${\bf C}P^2$ are integrable will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-284680