Isotropic Kahler immersions into a complex quadric

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紀要論文

We give another definition of a complex conformal structure on a complex quadric Q^n and introduce a (local) tensor field J which satisfies J^2=Id(the identity map). A complex subspace W of the tangent space T_pQ^n is called an isotropic complex subspace if JW is orthogonal to W. A Kahler immersion ψ: M^m→Q^n of an m-dimensional Kahler manifold M^m is said to be isotropic if for an arbitrary point p∈M, ψ*(T_pM) is an isotropic complex subspace in T_<ψ(p)>Q^n. We study the properties of higher fundamental forms of isotropic Kahler immersions and show some reduction theorems. Furthermore we construct isotropic Kahler immersions of Kahler C-spaces using orthogonal representations and study the higher normal spaces and the osculating degrees of isotropic Kahler immersions of Hermitian symmetric spaces.

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