梯度Ricci-Bourguignon孤立子的分裂定理

Splitting Theorem for Gradient Ricci-Bourguignon Solitons

摘要: 本文研究了完备梯度Ricci-Bourguignon孤立子的分裂性问题，证明了该孤立子的万有覆盖等距于${ℝ}^k\times {\mathbb{N}}^{n-k}$ 。同时，在数量曲率为常数且截面曲率满足有界性条件的假设下，证明了该孤立子的Ricci曲率核分布是平行的且具有整体常数秩。

Abstract: This paper investigates the splitting theorem of complete gradient Ricci-Bourguignon solitons. It is shown that the universal cover of such a soliton is isometric to ${ℝ}^k\times {\mathbb{N}}^{n-k}$ . Moreover, under the assumptions that the scalar curvature is constant and the sectional curvature satisfies a bounded condition, it is proved that the Ricci curvature kernel distribution of the soliton is parallel and has globally constant rank.