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Hypersurfaces immersed in a golden Riemannian manifold

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Abstract

The purpose of this paper is to study properties of hypersurfaces of a Riemannian manifold equipped with a golden structure. We discuss the necessary and sufficient conditions for a hypersurface to be a golden Riemannian manifold in terms of invariance. The totally geodesics and totally umbilical hypersurfaces in golden Riemannian manifolds are analyzed. Also, we construct an example on hypersurface of the Euclidean space endowed with a golden Riemannian structure.

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Acknowledgements

The authors are very much thankful to the referees for their valuable suggestions. Also authors would like to thank to Integral University, Lucknow, India, for providing the manuscript number IU/R&D/2018-MCN000449 to the present research work.

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  1. Department of Mathematics and Statistics, Faculty of Science, Integral University, Lucknow, 226026, India

    Mohammad Aamir Qayyoom & Mobin Ahmad

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  1. Mohammad Aamir Qayyoom
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  2. Mobin Ahmad
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Qayyoom, M.A., Ahmad, M. Hypersurfaces immersed in a golden Riemannian manifold. Afr. Mat. 33, 3 (2022). https://doi.org/10.1007/s13370-021-00954-x

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