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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.19 no.2 Temuco jun. 2017

http://dx.doi.org/10.4067/S0719-06462017000200033 

Articles

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

S. K. Yadav1 

S. K. Chaubey2 

D. L. Suthar3 

1 Poornima college of Engineering, Department of Mathematics, ISI-6, RIICO, Institutional Area, Sitapura, Jaipur-302022, Rajasthan, India. e-mail: prof_sky16@yahoo.com

2 Shinas College of Technology, Section of Mathematics, Department of Information Technology, Shinas, P.O. Box 77 Postal Code 324, Oman. e-mail: sk22_math@yahoo.co.in, sudhakar.chaubey@shct.edu.om

3 Wollo University, Department of Mathematics, P. O. Box: 1145, Dessie, South Wollo, Amhara Region, Ethiopia. dlsuthar@gmail.com

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.

Keywords and Phrases: η-Ricci solitons; gradient Ricci solitons; (LCS)n-manifold.

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.

2010 AMS Mathematics Subject Classification: 53C25, 53C15, 53C21.

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