<p>In this article, we study Riemann soliton on almost contact metric manifolds that fall in the Chinea–Gonzales class <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2853_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$C_5$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mn>5</mn> </msub> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2853_Article_IEq2.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$\oplus $</EquationSource> <EquationSource Format="MATHML"><math> <mo>⊕</mo> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2853_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">$C_{12}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mn>12</mn> </msub> </math></EquationSource> </InlineEquation>, also named <InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2853_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$C_5$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mn>5</mn> </msub> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq14"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2853_Article_IEq2.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$\oplus $</EquationSource> <EquationSource Format="MATHML"><math> <mo>⊕</mo> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq15"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2853_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">$C_{12}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mn>12</mn> </msub> </math></EquationSource> </InlineEquation>-manifolds. In particular, we consider a subclass of <InlineEquation ID="IEq16"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2853_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$C_5$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mn>5</mn> </msub> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq17"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2853_Article_IEq2.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$\oplus $</EquationSource> <EquationSource Format="MATHML"><math> <mo>⊕</mo> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq18"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2853_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">$C_{12}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mn>12</mn> </msub> </math></EquationSource> </InlineEquation>-manifolds namely <InlineEquation ID="IEq19"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2853_Article_IEq19.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-Kenmotsu manifolds, <InlineEquation ID="IEq20"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2853_Article_IEq19.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> being a smooth function. Certain results are correlated with generalized Sasakian-space-forms. The case of concircular potential vector field is critically analyzed with a supporting example.</p>

Riemann Solitons on $C_5$ $\oplus $ $C_{12}$-Spaces

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发表日期：

2025年5月18日

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Urmila Biswas,
Maria Falcitelli,
Avijit Sarkar

摘要

In this article, we study Riemann soliton on almost contact metric manifolds that fall in the Chinea–Gonzales class $C_5$ $C_{5}$ $\oplus $ $\oplus$ $C_{12}$ $C_{12}$ , also named $C_5$ $C_{5}$ $\oplus $ $\oplus$ $C_{12}$ $C_{12}$ -manifolds. In particular, we consider a subclass of $C_5$ $C_{5}$ $\oplus $ $\oplus$ $C_{12}$ $C_{12}$ -manifolds namely $\alpha $ $α$ -Kenmotsu manifolds, $\alpha $ $α$ being a smooth function. Certain results are correlated with generalized Sasakian-space-forms. The case of concircular potential vector field is critically analyzed with a supporting example.

Riemann Solitons on \(C_5\) \(\oplus \) \(C_{12}\)-Spaces

摘要