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Gradient solitons on statistical manifolds
Journal of Geometry and Physics ( IF 1.6 ) Pub Date : 2021-03-05 , DOI: 10.1016/j.geomphys.2021.104195 Adara M. Blaga , Bang-Yen Chen
中文翻译:
统计流形上的梯度孤子
更新日期:2021-03-18
Journal of Geometry and Physics ( IF 1.6 ) Pub Date : 2021-03-05 , DOI: 10.1016/j.geomphys.2021.104195 Adara M. Blaga , Bang-Yen Chen
We provide necessary and sufficient conditions for some particular couples of pseudo-Riemannian metrics and affine connections to be statistical structures if we have gradient almost Einstein, almost Ricci, almost Yamabe solitons, or a more general type of solitons on the manifold. In particular cases, we establish a formula for the volume of the manifold and give a lower and an upper bound for the norm of the Ricci curvature tensor field.
中文翻译:
统计流形上的梯度孤子
我们为某些特定夫妇提供必要和充分的条件 如果我们在流形上具有近似爱因斯坦,近似里奇,近似Yamabe孤子或更普通的孤子梯度,则将伪黎曼度量和仿射联系确定为统计结构。在特定情况下,我们为流形的体积建立一个公式,并给出Ricci曲率张量场范数的下限和上限。