Minimal two-spheres of low index in manifolds with positive complex sectional curvature
نویسنده
چکیده
Suppose that S is given a generic Riemannian metric with sectional curvatures which satisfy a suitable pinching condition formulated in terms of complex sectional curvatures. This pinching condition is satisfied by manifolds whose real sectional curvatures Kr(σ) satisfy 1/2 < Kr(σ) ≤ 1. Then the number of minimal two spheres of Morse index λ, for n − 2 ≤ λ ≤ 2n− 6, is at least p3(λ− n+ 2), where p3(k) is the number of k-cells in the Schubert cell decomposition for G3(R).
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