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- W3211846821 abstract "Abstract In this paper, we study $$eta$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>η</mml:mi> </mml:math> -Ricci solitons on almost cosymplectic $$(k,mu )$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>k</mml:mi> <mml:mo>,</mml:mo> <mml:mi>μ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -manifolds. As an application, it is proved that if an almost cosymplectic $$(k,mu )$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>k</mml:mi> <mml:mo>,</mml:mo> <mml:mi>μ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -metric with $$k<0$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo><</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> represents a Ricci soliton, then the potential vector field of the Ricci soliton is a strict infinitesimal contact transformation, and the corresponding almost cosymplectic manifold is locally isometric to a Lie group whose local structure is determined completely by $$k<0$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo><</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> . In addition, a concrete example is constructed to illustrate the above result." @default.
- W3211846821 created "2021-11-22" @default.
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- W3211846821 date "2021-11-08" @default.
- W3211846821 modified "2023-09-25" @default.
- W3211846821 title "Almost Cosymplectic $$(k,mu )$$-metrics as $$eta$$-Ricci Solitons" @default.
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- W3211846821 doi "https://doi.org/10.1007/s44198-021-00019-4" @default.
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