η-Ricci Solitons on 3-dimensional Trans-Sasakian Manifolds
Abstract In this paper, we study η-Ricci solitons on 3-dimensional trans-Sasakian manifolds. Firstly we give conditions for the existence of these geometric structures and then observe that they provide examples of η-Einstein manifolds. In the case of φ-Ricci symmetric tra...
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| Language: | English |
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Universidad de La Frontera. Departamento de Matemática y Estadística.
2020
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| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462020000100023 |
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| Summary: | Abstract In this paper, we study η-Ricci solitons on 3-dimensional trans-Sasakian manifolds. Firstly we give conditions for the existence of these geometric structures and then observe that they provide examples of η-Einstein manifolds. In the case of φ-Ricci symmetric trans-Sasakian manifolds, the η-Ricci soliton condition turns them to Einstein manifolds. Afterward, we study the implications in this geometric context of the important tensorial conditions R · S = 0, S · R = 0, W2 · S = 0 and S · W2 = 0. |
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