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manuscripta mathematica

, Volume 95, Issue 3, pp 295–310 | Cite as

Associated families of pluriharmonic maps¶and isotropy

  • J.-H. Eschenburg
  • R. Tribuzy

Abstract:

Like minimal surface immersions in 3-space, pluriharmonic maps into symmetric spaces allow a one-parameter family of isometric deformations rotating the differential (“associated family”); in fact, pluriharmonic maps are characterized by this property. We give a geometric proof of this fact and investigate the “isotropic” case where this family is constant. It turns out that isotropic pluriharmonic maps arise from certain holomorphic maps into flag manifolds. Further, we also consider higher dimensional generalizations of constant mean curvature surfaces which are Kähler submanifolds with parallel (1,1) part of their soecond fundamental form; under certain restrictions there are also characterized by having some kind of (“weak”) associated family. Examples where this family is constant arise from extrinsic Kähler symmetric spaces.

Mathematics Subject Classification (1991): 53C35, 53C42, 53J60 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • J.-H. Eschenburg
    • 1
  • R. Tribuzy
    • 2
  1. 1.Institut für Mathematik, Universität Augsburg, Universitätsstraße 12, D-86135 Augsburg, GermanyDE
  2. 2.Departamento de Matemática, Universidade do Amazonas, ICE, 69000 Manaus, AM., BrazilBR

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