Realizations of some contact metric manifolds as Ricci soliton real hypersurfaces
Realizations of some contact metric manifolds as Ricci soliton real hypersurfaces
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一些接触度量流形作为 Ricci 孤子实超曲面的实现
DOI：
10.1016/j.geomphys.2017.08.013
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Hiroshi Tamaru
中科院分区：
文献类型：
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作者：
Jong Taek Cho;Takahiro Hashinaga;Akira Kubo;Yuichiro Taketomi;Hiroshi Tamaru
Ghosh和Sharma最近研究了具有一定零条件的Ricci孤子接触度量流形。虽然梯度情况很好理解，但他们提供了非梯度情况的候选列表。这些候选者可以被实现为李群，但人们只知道底层李代数的结构，除了三维情况外，很难分析它们。本文研究了这些维数大于3的李群，并证明了连通、单连通和完全李群可以被实现为非紧实两平面Grassmannians中的齐次实超曲面。这些认识使我们能够，以一种谎言理论的方式，证明它们实际上都是利玛窦孤子。
Ricci soliton contact metric manifolds with certain nullity conditions have recently been studied by Ghosh and Sharma. Whereas the gradient case is well-understood, they provided a list of candidates for the nongradient case. These candidates can be realized as Lie groups, but one only knows the structures of the underlying Lie algebras, which are hard to be analyzed apart from the three-dimensional case. In this paper, we study these Lie groups with dimension greater than three, and prove that the connected, simply-connected, and complete ones can be realized as homogeneous real hypersurfaces in noncompact real two-plane Grassmannians. These realizations enable us to prove, in a Lie-theoretic way, that all of them are actually Ricci soliton.