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arXiv · 2610.34820

Constant Chern holomorphic sectional curvature on two-step solvmanifolds

Shanlin Guan·Yuqin Guo
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Abstract

Let $M=Γ\backslash G$ be a compact solvmanifold with a left-invariant Hermitian structure whose Lie algebra is two-step solvable. If the Chern holomorphic sectional curvature is constant, then the derived algebra is $J$-invariant and the Chern connection is flat. At the Lie-algebra level, we also prove that constant Chern holomorphic sectional curvature is impossible for a unimodular two-step solvable Hermitian Lie algebra of mixed Freibert-Swann type.

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Shanlin Guan, Yuqin Guo. 2026-10-26. Constant Chern holomorphic sectional curvature on two-step solvmanifolds. https://arxiv.org/abs/2610.34820

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