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Cubo (Temuco)

On-line version ISSN 0719-0646

Cubo vol.22 no.1 Temuco Apr. 2020

http://dx.doi.org/10.4067/S0719-06462020000100023 

Articles

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

Sampa Pahan1 

1Department of Mathematics, Mrinalini Datta Mahavidyapith Kolkata-700051, India. sampapahan25@gmail.com

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.

Keywords and Phrases: Trans-Sasakian manifold; η-Ricci solitons.

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.

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

Acknowledgement:

The author wish to express her sincere thanks and gratitude to the referee for valuable suggestions towards the improvement of the paper.

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