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<p>The aim of this paper is to study pointwise quasi bi-slant submanifolds within the context of metallic Rimannian manifolds by integrating the concepts of pointwise slant submanifolds, de Rham cohomology and warped products. We begin by defining pointwise quasi bi-slant submanifolds, followed by deriving necessary and sufficient conditions for the integrability and minimality of the distributions involved, their geodesic behaviour, and the characterization of mixed totally geodesic distributions. A significant contribution of this work is the discussion of the de Rham cohomology and warped product structures of these submanifolds, which connect their geometric structures with intrinsic topological invariants. Alongside we provide supportive non-trivial examples to validate the theory. These results provide a significant advancement in the study of Riemannian submanifolds and its applications.</p>

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Pointwise quasi bi-slant submanifolds, de Rham cohomology and their warped products in metallic Riemannian manifolds

  • 期刊论文

  • 发表日期：

    2026年1月4日

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  • Harmandeep Kaur,
  • Gauree Shanker,
  • Ankit Yadav

摘要

The aim of this paper is to study pointwise quasi bi-slant submanifolds within the context of metallic Rimannian manifolds by integrating the concepts of pointwise slant submanifolds, de Rham cohomology and warped products. We begin by defining pointwise quasi bi-slant submanifolds, followed by deriving necessary and sufficient conditions for the integrability and minimality of the distributions involved, their geodesic behaviour, and the characterization of mixed totally geodesic distributions. A significant contribution of this work is the discussion of the de Rham cohomology and warped product structures of these submanifolds, which connect their geometric structures with intrinsic topological invariants. Alongside we provide supportive non-trivial examples to validate the theory. These results provide a significant advancement in the study of Riemannian submanifolds and its applications.