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Quasi Hemi-Slant Submanifolds of Metallic Riemannian Manifolds

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Abstract

In this paper, we present the general notion of quasi hemi-slant submanifolds of metallic Riemannian manifolds. We study some properties of submanifolds, specially quasi hemi-slant submanifolds of metallic and golden Riemannian manifolds. We obtain some necessary and sufficient conditions for submanifolds to be quasi hemi-slant in metallic and golden Riemannian manifolds and also obtain integrability conditions for the distributions. At last, we construct an example of a quasi hemi-slant submanifold of a metallic Riemannian manifold.

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Acknowledgements

The first author has been sponsored by University Grants Commission (UGC) Senior Research Fellowship, India. UGC-Ref. No.: 1139/(CSIR-UGC NET JUNE 2018).

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Authors and Affiliations

  1. Department of Mathematics, Jadavpur University, Kolkata, 700032, India

    Payel Karmakar & Arindam Bhattacharyya

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  1. Payel Karmakar
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  2. Arindam Bhattacharyya
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Correspondence to Payel Karmakar.

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Significance of the work

The theory of submanifolds has the origin in the study of geometry of plane curves initiated by Fermat. Nowadays, it has gained prominence in computer design, image processing, economic modeling, mathematical physics and mechanics except modern differential geometry. Also, according to De Spinadel, besides carrying the name of metals, the metallic means family have common mathematical properties that attach a fundamental importance to them in modern investigations about the search of universal roads to chaos, and the metallic numbers found many applications in researches that analyse the behaviour of non linear dynamical systems when they proceed from a periodic regime to a chaotic one. Golden mean is known from ancient times as an expression of harmony of many constructions, paintings and music. It also appears as an expression of the objects from the natural world (flowers, trees, fruits) possessing pentagonal symmetry.

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Karmakar, P., Bhattacharyya, A. Quasi Hemi-Slant Submanifolds of Metallic Riemannian Manifolds. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 94, 75–82 (2024). https://doi.org/10.1007/s40010-023-00826-y

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  • DOI: https://doi.org/10.1007/s40010-023-00826-y

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