Minimal two-spheres of low index in manifolds of positive complex sectional curvature

2014/09/12 by Moore, John Douglas, Ream, Robert · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1409.3872

Abstract

Suppose that Sⁿ 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 K_r(σ) satisfy 1/2 lt; K_r(σ) ≤ 1. Then the number of minimal two spheres of Morse index λ, for n-2 ≤ λ≤ 2n-5, is at least p₃(λ-n+2), where p₃(k) is the number of k-cells in the Schubert cell decomposition for G₃(\mathbb Rⁿ⁺¹).

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