Recent interest among geometers in f-structures of K. Yano is due to the study of topology and dynamics of contact foliations and generalized A. Weinstein conjectures. Weak metric f-structures, introduced by the author and R. Wolak as a generalization of Hermitian structure, as well as f-structure allow for a fresh perspective on the classical theory. An important case of such manifolds, which is locally a twisted product, is a weak <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\beta f$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>β</mi> <mi>f</mi> </mrow> </math></EquationSource> </InlineEquation>-Kenmotsu manifold defined as a generalization of K. Kenmotsu’s concept. In this paper, the concept of the <InlineEquation ID="IEq8"> <EquationSource Format="TEX"></EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-Ricci tensor of S. Tashibana is adapted to weak metric f-manifolds, the interaction of <InlineEquation ID="IEq9"> <EquationSource Format="TEX"></EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-<InlineEquation ID="IEq10"> <EquationSource Format="TEX">$\eta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>-Ricci soliton with the weak <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$\beta f$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>β</mi> <mi>f</mi> </mrow> </math></EquationSource> </InlineEquation>-Kenmotsu structure is studied and new characteristics of <InlineEquation ID="IEq12"> <EquationSource Format="TEX">$\eta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>-Einstein metrics are obtained.

$*$-$\eta $-Ricci solitons on weak metric f-manifolds

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2025年11月6日

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Vladimir Rovenski

摘要

Recent interest among geometers in f-structures of K. Yano is due to the study of topology and dynamics of contact foliations and generalized A. Weinstein conjectures. Weak metric f-structures, introduced by the author and R. Wolak as a generalization of Hermitian structure, as well as f-structure allow for a fresh perspective on the classical theory. An important case of such manifolds, which is locally a twisted product, is a weak $\beta f$ $β f$ -Kenmotsu manifold defined as a generalization of K. Kenmotsu’s concept. In this paper, the concept of the $*$ $*$ -Ricci tensor of S. Tashibana is adapted to weak metric f-manifolds, the interaction of $*$ $*$ - $\eta $ $η$ -Ricci soliton with the weak $\beta f$ $β f$ -Kenmotsu structure is studied and new characteristics of $\eta $ $η$ -Einstein metrics are obtained.

\(*\)-\(\eta \)-Ricci solitons on weak metric f-manifolds

摘要