AI 中文总结
该研究对配备标准齐性黎曼度量的复流形M = SU(n+2)/S(U(1)×U(1)×U(n))的极大全测地子流形进行分类，通过自然纤维化与曲率计算完成分类，得到含多种类型子流形的完整描述。
AI 中文摘要
本研究对复流形M = SU(n+2)/S(U(1)×U(1)×U(n)) ≅ F_{1,2}(ℂ^{n+2})（n≥2，配备标准齐性黎曼度量）的极大全测地子流形进行分类。利用自然纤维化S²→M→G₂(ℂ^{n+2})及基于奥尼尔公式推导的曲率计算，我们识别出切表示的曲率不变子空间，进而完整描述了M的极大全测地子流形，包括低维复格拉斯曼流形的扭子空间、实旗流形、复射影空间的乘积及四元数射影空间的扭子空间。
英文摘要
This work presents a classification of the maximal totally geodesic submanifolds of the complex manifold M = SU(n+2)/S(U(1) x U(1) x U(n)) \cong F_{1,2}(\mathbb{C}^{n+2}), n\geq 2, equipped with its standard homogeneous Riemannian metric. Using the natural fibration S^2 \to M \to G_2(\mathbb{C}^{n+2}) and curvature computations derived from O'Neill's formulas, we identify curvature-invariant subspaces of the tangent representation. As a consequence, we obtain a complete description of the maximal totally geodesic submanifolds of M. These include twistor spaces of lower-dimensional complex Grassmannians, real flag manifolds, products of complex projective spaces, and twistor spaces of quaternionic projective spaces.
