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<p>We establish a general inequality and optimal inequalities involving the normalized Casorati curvatures and the generalized normalized Casorati curvatures within the horizontal space of a Riemannian map from a Riemannian manifold to a nearly Kaehler manifold with a constant holomorphic sectional curvature. Riemannian maps serve as generalizations of isometric immersions and Riemannian submersions. Consequently, we extend these inequalities to encompass Riemannian submanifolds within nearly Kaehler manifolds with a constant holomorphic sectional curvature.</p>

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Optimal inequalities involving Casorati curvatures for Riemannian maps to nearly Kaehler manifolds

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月3日

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  • Tanveer Fatima,
  • Reetu Maini,
  • Garima Gupta,
  • Rakesh Kumar,
  • Rashmi Sachdeva,
  • Rachna Rani

摘要

We establish a general inequality and optimal inequalities involving the normalized Casorati curvatures and the generalized normalized Casorati curvatures within the horizontal space of a Riemannian map from a Riemannian manifold to a nearly Kaehler manifold with a constant holomorphic sectional curvature. Riemannian maps serve as generalizations of isometric immersions and Riemannian submersions. Consequently, we extend these inequalities to encompass Riemannian submanifolds within nearly Kaehler manifolds with a constant holomorphic sectional curvature.