论文标题
梯度Yamabe solitons的一些特征
Some characterizations of gradient Yamabe solitons
论文作者
论文摘要
在本文中，我们证明了满足某些其他条件的梯度Yamabe Soliton必须具有恒定的标态曲率。后来，我们表明，在梯度扩展或稳定的Yamabe soliton中，如果潜在函数满足某些积分条件，则具有非负RICCI曲率的曲率，则它是次谐波的，特别是对于稳定的情况，潜在函数会变为谐波。另外，我们已经证明，在紧凑的Yamabe Soliton中，潜在函数与Hodge-De Rham电位一致，直至常数。
In this article we have proved that a gradient Yamabe soliton satisfying some additional conditions must be of constant scalar curvature. Later, we have showed that in a gradient expanding or steady Yamabe soliton with non-negative Ricci curvature if the potential function satisfies some integral condition then it is subharmonic, in particular, for steady case the potential function becomes harmonic. Also we have proved that, in a compact gradient Yamabe soliton, the potential function agrees with the Hodge-de Rham potential upto a constant.
