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<p>This paper introduces a new class of geometric mappings called pointwise almost h-conformal semi-slant Riemannian maps (pahcssR maps) between Riemannian manifolds and almost quaternionic Hermitian manifolds. These maps unify and extend existing concepts like Riemannian submersions, conformal maps, and semi-slant submersions to the quaternionic setting. We establish fundamental properties and provide necessary and sufficient conditions for these maps to be harmonic or totally geodesic. We also investigate the decomposition of the tangent bundle and analyze the geometric behavior of the associated distributions. Several illustrative examples are provided to support the theoretical framework. Finally, we discuss potential applications in mathematical physics, where quaternionic structures are prevalent in theories such as supergravity and string theory.</p>

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On the pahcssR maps to almost quaternionic Hermitian manifolds

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Kwang Soon Park

摘要

This paper introduces a new class of geometric mappings called pointwise almost h-conformal semi-slant Riemannian maps (pahcssR maps) between Riemannian manifolds and almost quaternionic Hermitian manifolds. These maps unify and extend existing concepts like Riemannian submersions, conformal maps, and semi-slant submersions to the quaternionic setting. We establish fundamental properties and provide necessary and sufficient conditions for these maps to be harmonic or totally geodesic. We also investigate the decomposition of the tangent bundle and analyze the geometric behavior of the associated distributions. Several illustrative examples are provided to support the theoretical framework. Finally, we discuss potential applications in mathematical physics, where quaternionic structures are prevalent in theories such as supergravity and string theory.