Resumen de Some geometric properties of η Ricci solitons and gradient Ricci solitons on (lcs) n -manifolds

Sunil Kumar Yadav, S. K. Chaubey, D.L. Suthar

• español

  Resumen: En el contexto de geometría para-contacto Hausdorff, consideramos η-Ricci solitones y Ricci solitones gradientes en variedades. Establecemos que en una (LCS)n-variedad (M, ϕ, ξ, η, 𝑔), la existencia de un η-Ricci solitón implica que (M, 𝑔) es casi-Einstein. Encontramos condiciones para que los Ricci solitones en una (LCS)n-variedad (M, ϕ, ξ, η, 𝑔) sean contractivos, estables o expansivos. Al concluir, mostramos ejemplos de dichas variedades con η-Ricci solitones.

• English

  Abstract: In the context of para-contact Hausdorff geometry η-Ricci solitons and gradient Ricci solitons are considered on manifolds. We establish that on an (LCS)n-manifold (M, ϕ, ξ, η, 𝑔), the existence of an ηRicci soliton implies that (M, 𝑔) is quasi-Einstein. We find conditions for Ricci solitons on an (LCS)n-manifold (M, ϕ, ξ, η, 𝑔) to be shrinking, steady and expanding. At the end we show examples of such manifolds with η-Ricci solitons.