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Holomorphic isometries of twistor spaces

โœ Scribed by Costantino Medori; Adriano Tomassini

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
72 KB
Volume
42
Category
Article
ISSN
0393-0440

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โœฆ Synopsis

Let Z g (M) be the twistor space over an oriented 2n-dimensional Riemannian manifold (M, g) with nonpositive and parallel Ricci tensor. Let h and J be the natural metric and almost complex structure on Z g (M), respectively. We prove that any isometry of the twistor space Z g (M) preserves the horizontal and vertical distributions. When M is compact, we give an estimate of the dimension of the groups of isometries and holomorphic isometries on the twistor space. In particular, if M is a compact almost Kรคhler manifold with the same properties of curvature and the Ricci tensor is negative, then the group of the holomorphic isometries is finite.

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