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<p>This study explores conjugate connections on Riemannian manifolds, with a focus on the quarter-symmetric recurrent metric connection. We introduce and analyze conjugate quarter-symmetric recurrent metric connection and explore its geometric properties including torsion tensor, metric compatibility, curvature behavior and conditions for Ricci solitons. Furthermore, we investigate semi-conjugate and generalized conjugate quarter-symmetric recurrent metric connection and study its detailed overview of characteristics and implications properties. The work also presents new results on the characterization of Ricci solitons in various settings such as <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(W_i\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>W</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation>-flat and concircular flat manifolds and identifies conditions under which the manifold becomes quasi-Einstein or hyper-generalized quasi-Einstein. These findings generalize and unify several earlier results on symmetric and non-symmetric connections.</p>

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Conjugate Quarter-symmetric Recurrent Metric Connections and Ricci Solitons on Riemannian Manifolds

  • 期刊论文

  • 发表日期：

    2026年8月1日

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  • Rajesh Kumar,
  • Lalthanpuia Chhangte,
  • Lalrinfeli Lianhna

摘要

This study explores conjugate connections on Riemannian manifolds, with a focus on the quarter-symmetric recurrent metric connection. We introduce and analyze conjugate quarter-symmetric recurrent metric connection and explore its geometric properties including torsion tensor, metric compatibility, curvature behavior and conditions for Ricci solitons. Furthermore, we investigate semi-conjugate and generalized conjugate quarter-symmetric recurrent metric connection and study its detailed overview of characteristics and implications properties. The work also presents new results on the characterization of Ricci solitons in various settings such as \(W_i\) W i -flat and concircular flat manifolds and identifies conditions under which the manifold becomes quasi-Einstein or hyper-generalized quasi-Einstein. These findings generalize and unify several earlier results on symmetric and non-symmetric connections.