论文标题
卡坦 - 哈达玛歧管的等轴测定理
Isometry theorem of Cartan-Hadamard manifold
论文作者
论文摘要
卡坦 - 哈达马德歧管是具有非阳性截面曲率的简单连接的riemannian歧管。在本文中，我们已经证明，具有潜在功能不可或缺的稳定梯度RICCI Soliton满足稳定梯度的cartan-hadamard歧管是欧几里得空间的等值线。接下来，我们证明了一种紧凑的定理，用于梯度收缩Ricci soliton满足某些标量曲率条件。最后，我们已经表明，具有线性体积生长和正势功能的梯度扩展的Ricci Soliton是爱因斯坦歧管。
Cartan-Hadamard manifold is a simply connected Riemannian manifold with non-positive sectional curvature. In this article, we have proved that a Cartan-Hadamard manifold satisfying steady gradient Ricci soliton with the integral condition of potential function is isometric to the Euclidean space. Next we have proved a compactness theorem for gradient shrinking Ricci soliton satisfying some scalar curvature condition. Finally, we have showed that a gradient expanding Ricci soliton with linear volume growth and positive potential function is an Einstein manifold.
