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Types of Submanifolds in Metallic Riemannian Manifolds: A Short Survey

Author

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  • Cristina E. Hretcanu

    (Faculty of Food Engineering, Stefan cel Mare University of Suceava, 720229 Suceava, Romania
    These authors contributed equally to this work.)

  • Adara M. Blaga

    (Faculty of Mathematics and Computer Science, West University of Timisoara, 300223 Timisoara, Romania
    These authors contributed equally to this work.)

Abstract

We provide a brief survey on the properties of submanifolds in metallic Riemannian manifolds. We focus on slant, semi-slant and hemi-slant submanifolds in metallic Riemannian manifolds and, in particular, on invariant, anti-invariant and semi-invariant submanifolds. We also describe the warped product bi-slant and, in particular, warped product semi-slant and warped product hemi-slant submanifolds in locally metallic Riemannian manifolds, obtaining some results regarding the existence and nonexistence of non-trivial semi-invariant, semi-slant and hemi-slant warped product submanifolds. We illustrate all these by suitable examples.

Suggested Citation

  • Cristina E. Hretcanu & Adara M. Blaga, 2021. "Types of Submanifolds in Metallic Riemannian Manifolds: A Short Survey," Mathematics, MDPI, vol. 9(19), pages 1-22, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2467-:d:649242
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    References listed on IDEAS

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    3. Falleh R. Al-Solamy & Meraj Ali Khan, 2012. "Warped Product Submanifolds of Riemannian Product Manifolds," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, November.
    4. Falcón, Sergio & Plaza, Ángel, 2008. "On the 3-dimensional k-Fibonacci spirals," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 993-1003.
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