Abstract
In the Grassmann manifold G +2,n of bivectors (n≥4), the sectional curvature K(σ) in the direction of a 2-plane σ takes values in [0,2]. All stationary values a of K(σ) such that the gradient ∇K|σ=σ0 vanishes for at least one σ0 ∈ K−1(a) are found. The values are {0,1,2} for n=4, {0,1/5,1,2} for n=5, and {0,1/5,1/2,1,2} for n≥6. Bibliography: 7 titles.
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Kozlov, S.E. Stationary Values of Sectional Curvature in Grassmann Manifolds of Bivectors. Journal of Mathematical Sciences 110, 2810–2819 (2002). https://doi.org/10.1023/A:1015302312768
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DOI: https://doi.org/10.1023/A:1015302312768