AI 中文总结
本文证明了标准2n-球面中线性满的 branched 极小2-球面的 Morse 指标和零化度的尖锐界，并推广到全迷向曲面。
AI 中文摘要
我们证明了在标准2n-球面中线性满的 branched 极小2-球面的 Morse 指标和零化度的尖锐上下界。特别地，我们证明了标准2n-球面中线性满的极小2-球面的 Morse 指标至少为 n(n-1)(2n+1)，且等号成立当且仅当该2-球面与 Boruvka 球面 twistor 等价。我们的技术也更一般地适用于给出2n-球面中全迷向曲面的 Morse 指标和零化度的界。
英文摘要
We prove sharp upper and lower bounds for the Morse index and nullity of linearly full branched minimal 2-spheres in the round 2n-sphere. In particular, we show that the Morse index of a linearly full minimal 2-sphere in the round 2n-sphere is at least n(n-1)(2n+1), with equality if and only if the 2-sphere is twistor-equivalent to the Boruvka sphere. Our techniques also apply more generally to give bounds for the Morse index and nullity for totally isotropic surfaces in the 2n-sphere.
Comments37 pages
