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869 spherical and hyperbolic space. It is divided into two equal-sized parts: the first is devoted to the two-dimensional case, where much more is known than in the n-dimensional setting, which is discussed in the second part. In addition, there is an appendix providing some important background information, essentially from convex geometry. Many of the(More)
Harmonic morphisms are mappings between Riemann-ian manifolds which preserve Laplace's equation. They can be characterized as harmonic maps which enjoy an extra property called horizontal weak conformality or semiconformality. We shall give a brief survey of the theory concentrating on (i) twistor methods , (ii) harmonic morphisms with one-dimensional(More)
619 with minimal surfaces. It requires a knowledge of basic differential geometry and a little representation theory. It should certainly be bought by any library where there is some interest in the above named subjects and also by individuals who research in harmonic maps or related fields—though those with a lesser interest may find it too specialized to(More)
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(More)
We show that Jacobi fields along harmonic maps between suitable spaces preserve conformality, holomorphicity, real isotropy and complex isotropy to first order; this last being one of the key tools in the proof by Lemaire and the author of integrability of Jacobi fields along harmonic maps from the 2-sphere to the complex projective plane.
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 4πE 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(More)