Let M be a real hypersurface in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\mathbb {C}P^n$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">C</mi> <msup> <mi>P</mi> <mi>n</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> or <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathbb {C}H^n$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">C</mi> <msup> <mi>H</mi> <mi>n</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$n\ge 2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> admitting a generalized Ricci almost soliton with Reeb potential vector field. In this paper, it is proved that if M is Hopf, then it is locally congruent to type <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$(A_0)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>A</mi> <mn>0</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> or <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$(A_1)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>A</mi> <mn>1</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> hypersurfaces. Moreover, we give two nonexistence results of some special non-Hopf real hypersurfaces in <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\mathbb {C}P^2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">C</mi> <msup> <mi>P</mi> <mn>2</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> or <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\mathbb {C}H^2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">C</mi> <msup> <mi>H</mi> <mn>2</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> admitting a generalized Ricci almost soliton with Reeb potential vector field.

Generalized Ricci almost solitons on real hypersurfaces with Reeb potential vector field

期刊论文
发表日期：

2025年10月22日

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Yaning Wang

摘要

Let M be a real hypersurface in $\mathbb {C}P^n$ $C P^{n}$ or $\mathbb {C}H^n$ $C H^{n}$ with $n\ge 2$ $n \geq 2$ admitting a generalized Ricci almost soliton with Reeb potential vector field. In this paper, it is proved that if M is Hopf, then it is locally congruent to type $(A_0)$ $(A_{0})$ or $(A_1)$ $(A_{1})$ hypersurfaces. Moreover, we give two nonexistence results of some special non-Hopf real hypersurfaces in $\mathbb {C}P^2$ $C P^{2}$ or $\mathbb {C}H^2$ $C H^{2}$ admitting a generalized Ricci almost soliton with Reeb potential vector field.