Ricci solitons on low-dimensional generalized symmetric spaces

详细信息    查看全文

• 作者：Giovanni Calvaruso^a ; ^{giovanni.calvaruso@unisalento.it} ; Eugenia Rosado^b ; ^{eugenia.rosado@upm.es}
• 关键词：53C50 ; 53B30 ; 35A01
• 刊名：Journal of Geometry and Physics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：112
• 期：Complete
• 页码：106-117
• 全文大小：458 K
• 卷排序：112

文摘

We consider three- and four-dimensional pseudo-Riemannian generalized symmetric spaces, whose invariant metrics were explicitly described in Černý and Kowalski (1982). While four-dimensional pseudo-Riemannian generalized symmetric spaces of types AA, CC and DD are algebraic Ricci solitons, the ones of type BB are not so. The Ricci soliton equation for their metrics yields a system of partial differential equations. Solving such system, we prove that almost all the four-dimensional pseudo-Riemannian generalized symmetric spaces of type BB are Ricci solitons. These examples show some deep differences arising for the Ricci soliton equation between the Riemannian and the pseudo-Riemannian cases, as any homogeneous Riemannian Ricci soliton is algebraic Jablonski (2015). We also investigate three-dimensional generalized symmetric spaces of any signature and prove that they are Ricci solitons.