The Twistor Method

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


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.


Principal Bundle Conformal Immersion Twistor Bundle Conformal Minimal Immersion Darboux Frame 
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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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