The Twistor Method

  • Kichoon Yang
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 54)

Abstract

Let N be an oriented 2n—dimensional Riemannian manifold and also let SO(N) → N denote the SO(2n)—principal bundle of oriented orthonormal frames over N. The associated fibre bundle
$$ SO(N){{ \times }_{{SO(2n)}}}SO(2n)/U(n) = SO(N)/U(n) $$
is called the orthogonal twistor bundle over N. The fibre at x ∈ N parametrizes the set of all orientation-preserving orthogonal complex structures of the vector space TxN. T= SO(N)/U(n) can be made into an almost complex manifold. In fact there are 2γ, γ = n(n−1)/2, many natural almost complex structures on T. (See §2 for the description.) And one attempts to study minimal surfaces in N in terms of complex curves in T.

Keywords

Principal Bundle Conformal Immersion Twistor Bundle Conformal Minimal Immersion Darboux Frame 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Kichoon Yang
    • 1
  1. 1.Department of MathematicsArkansas State UniversityUSA

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