η-Ricci Solitons on 3-dimensional Trans-Sasakian Manifolds

• Autores: Sampa Pahan
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 22, Nº. 1, 2020, págs. 23-37
• Idioma: inglés
• DOI: 10.4067/S0719-06462020000100023
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• Resumen
  • español

    Resumen En este artículo estudiamos solitones η-Ricci en variedades trans-Sasakianas tridimensionales. En primer lugar damos condiciones para la existencia de estas estructuras geométricas y luego observamos que ellas dan ejemplos de variedades η-Einstein. En el caso de variedades trans-Sasakianas φ-Ricci simétricas, la condición de solitón η-Ricci las convierte en variedades Einstein. A continuación estudiamos las implicancias en este contexto geométrico de las importantes condiciones tensoriales R · S = 0, S · R = 0, W2 · S = 0 y S · W2 = 0.

  • English

    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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