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<p>Weak almost contact metric manifolds (i.e., the complex structure is replaced by a nonsingular skew-symmetric tensor), defined by the author and R.&#xa0;Wolak, allow a new look at the classical theory and find novel applications in mathematics and physics. An important case of these manifolds, which is locally a twisted product, is a weak <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>-Kenmotsu manifold defined by the author and D.S.&#xa0;Patra. In the paper, the concept of the <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-Ricci tensor is adapted to weak almost contact manifolds, the interaction of the <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-<InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(\eta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>-Ricci soliton with the weak <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>-Kenmotsu structure is studied and new characteristics of Einstein metrics are&#xa0;obtained.</p>

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\(*\)-\(\eta \)-Ricci solitons and Einstein metrics on a weak \(\beta \)-Kenmotsu manifold

  • 期刊论文

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  • 发表日期：

    2026年2月5日

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  • Vladimir Rovenski

摘要

Weak almost contact metric manifolds (i.e., the complex structure is replaced by a nonsingular skew-symmetric tensor), defined by the author and R. Wolak, allow a new look at the classical theory and find novel applications in mathematics and physics. An important case of these manifolds, which is locally a twisted product, is a weak \(\beta \) β -Kenmotsu manifold defined by the author and D.S. Patra. In the paper, the concept of the \(*\) ∗ -Ricci tensor is adapted to weak almost contact manifolds, the interaction of the \(*\) ∗ - \(\eta \) η -Ricci soliton with the weak \(\beta \) β -Kenmotsu structure is studied and new characteristics of Einstein metrics are obtained.