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<p>The study of quaternionic space forms is important because it provides a natural setting for investigating geometric structures with rich symmetry properties, extending Riemannian and Kählerian geometries. In this paper, we establish relationships between intrinsic and extrinsic geometric properties, including Chen and generalized Euler inequalities, for submanifolds in quaternionic space forms equipped with a semi-symmetric non-metric connection. The proofs make use of the notion of sectional curvature of a semi-symmetric non-metric connection and its fundamental properties, which was recently defined by A. Mihai and the second author.</p>

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Certain Invariants and Inequalities in Quaternionic Geometry Endowed with a Semi-Symmetric Non-Metric Connection

  • 期刊论文

  • 发表日期：

    2025年11月24日

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  • Mohammed Mohammed,
  • Ion Mihai,
  • Simona Costache,
  • Jesse Alt,
  • Samuel Ssekajja

摘要

The study of quaternionic space forms is important because it provides a natural setting for investigating geometric structures with rich symmetry properties, extending Riemannian and Kählerian geometries. In this paper, we establish relationships between intrinsic and extrinsic geometric properties, including Chen and generalized Euler inequalities, for submanifolds in quaternionic space forms equipped with a semi-symmetric non-metric connection. The proofs make use of the notion of sectional curvature of a semi-symmetric non-metric connection and its fundamental properties, which was recently defined by A. Mihai and the second author.