考虑度量满足规范ε-Ricci流的闭的n维黎曼流形,给出一类几何算子-Δ+cR的特征值的发展方程,其中常数c≥1/4,R是流形上的数量曲率。作为应用,在闭曲面上证明了这类几何算子的特征值沿着规范ε-Ricci流保持单调性,从而推广了前人的相关研究结果。 
  关键词规范ε-Ricci流;特征值;单调性;几何算子
中图分类号O186.1 文献标识码A 文章编号 295-2457(217)32-17-2
AbstractAn n dimensional closed Riemannian manifold with the metric which satisfied the normalizedε-Ricci flow will be considered in the paper. The evolution of eigenvalues for geometric operator will be obtained. As an application, along the normalizedε-Ricci flow the monotonicity of eigenvalues can be proved on closed surfaces. These results generalizes our predecessors’ results on Ricci flow.
Key wordsThe normalizedε-Ricci flow; Eigenvalue; Monotonicity; Geometric operator
1 预备知识
3 结语
本文利用几何分析的方法,对规范ε-Ricci流下一类常见的几何算子的特征值进行研究,得到了闭曲面上该算子特征值的单调性。文中的结果推广了文献4中的相关结果,也对ε-Ricci流及流形上几何算子特征值相关问题的进一步研究有很好的启发意义。
参考文献
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