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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2024 Volume 115, Issue 2, Pages 240–257 (Mi mzm13989)

Papers published in the English version of the journal

Ricci Solitons on Generalized Sasakian Space Forms with Kenmotsu Metric

S. Rani, R. Gupta

Guru Gobind Singh Indraprastha University, University School of Basic and Applied Sciences, New Delhi

Abstract: We study Ricci solitons and $*$-Ricci solitons on generalized Sasakian space forms (GSSF) $M^{2 n+1}(f_1, f_2, f_3)$ with parallel $*$-Ricci tensor. We prove that if a GSSF $M^{2 n+1}(f_1, f_2, f_3)$ with the Kenmotsu metric admits a Ricci soliton or a $*$-Ricci soliton, then $f_1=-1$ and $f_2=f_3=0$. Moreover, the Ricci soliton is expanding, and the $*$-Ricci soliton is steady. Further, we provide some examples.

Keywords: generalized Sasakian space form, Ricci soliton, $*$-Ricci soliton, Kenmotsu manifold, conformal Killing vector field.

MSC: 53C15, 53C40, 53C50, 53D15

Received: 15.04.2023

Language: English


 English version:
Mathematical Notes, 2024, 115:2, 240–257

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© Steklov Math. Inst. of RAS, 2024