Copyright © 2010 Bruno Ascenso Simões. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The use of twistor methods in the study of Jacobi fields has proved quite fruitful,
leading to a series of results. L. Lemaire and J. C. Wood proved several properties of Jacobi fields
along harmonic maps from the two-sphere to the complex projective plane and to the three- and four-dimensional spheres, by carefully relating the infinitesimal deformations of the harmonic maps to
those of the holomorphic data describing them. In order to advance this programme, we prove a
series of relations between infinitesimal properties of the map and those of its twistor lift. Namely,
we prove that isotropy and harmonicity to first order of the map correspond to holomorphicity to
first order of its lift into the twistor space, relatively to the standard almost complex structures
and . This is done by obtaining first-order analogues of classical twistorial constructions.