论文标题
带有广义的Ricci Solitons的扩展的准元素歧管
The extended quasi-Einstein manifolds with generalised Ricci solitons
论文作者
论文摘要
作为爱因斯坦歧管的概括，几乎准代因歧管和伪准代因歧管在研究一般相对论方面都很有趣且有用。在本文中，我们研究了源自伪准代因歧管的延长的准元素歧管。在显示了延长的准元素歧管的存在定理之后，我们给出了这种歧管的一些特殊几何特性。同时，我们还与某些孤子（如广义Ricci Soliton或Riemann Soliton）讨论了扩展的准元素歧管。此外，我们构建了一些非平凡的例子，以说明这些扩展的准元素歧管。
As a generalization of Einstein manifolds, the nearly quasi-Einstein manifolds and pseudo quasi-Einstein manifolds are both interesting and useful in studying the general relativity. In this paper, we study the extended quasi-Einstein manifolds which derive from pseudo quasi-Einstein manifolds. After showing the existence theorem of extended quasi-Einstein manifold, we give some special geometric properties of such manifolds. At the same time, we also discuss the extended quasi-Einstein manifolds with certain soliton like generalised Ricci soliton or Riemann soliton. Furthermore, we construct some nontrivial example to illustrate these extended quasi-Einstein manifolds.
