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<p>This paper investigates submanifolds immersed in a conformal Kenmotsu space form endowed with a quarter-symmetric connection recently considered by Qu and Wang (J Math Anal Appl 431(2):955–987. 2015). By employing the concept of generalized normalized <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\delta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-Casorati curvature in conjunction with scalar curvature, we establish sharp and optimal inequalities that clarify the relationship between the intrinsic and extrinsic geometry of the submanifold. Furthermore, we explore the equality cases of these inequalities, discuss their geometric implications and deduce several consequences. To substantiate the theoretical developments, we construct two explicit examples to illustrate the validity and applicability of the derived results.</p>

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Curvature Inequalities for Submanifolds in Conformal Kenmotsu Space Forms with Quarter-Symmetric Connection

  • 期刊论文

  • 发表日期：

    2026年2月27日

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  • Md Aquib,
  • Ibrahim Al-Dayel,
  • Alina-Daniela Vîlcu,
  • Gabriel-Eduard Vîlcu

摘要

This paper investigates submanifolds immersed in a conformal Kenmotsu space form endowed with a quarter-symmetric connection recently considered by Qu and Wang (J Math Anal Appl 431(2):955–987. 2015). By employing the concept of generalized normalized \(\delta \) δ -Casorati curvature in conjunction with scalar curvature, we establish sharp and optimal inequalities that clarify the relationship between the intrinsic and extrinsic geometry of the submanifold. Furthermore, we explore the equality cases of these inequalities, discuss their geometric implications and deduce several consequences. To substantiate the theoretical developments, we construct two explicit examples to illustrate the validity and applicability of the derived results.