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\(\zeta \)-Ricci Soliton on Real Hypersurfaces of Nearly Kaehler 6-Sphere with SSMC

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Abstract

The main intention of this paper is to study the real hypersurfaces in nearly Kaehler \(\mathbb {S}^{6}\) endowed with a semi-symmetric metric connection. We characterize the real hypersurfaces of the nearly Kaehler \(\mathbb {S}^{6}\) admitting semi-symmetric metric connection, and investigate the curvature properties of these submanifolds. Moreover, it is shown that a real hypersurface is congruent to an open segment of a totally-geodesic hypersphere or a tube over an almost complex curve in \(\mathbb {S}^{6}\) if such a connected real hypersurface of nearly Kaehler \(\mathbb {S}^{6}\) is an \(\zeta \)-Ricci soliton with the potential vector field \(\xi \).

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Authors and Affiliations

  1. Department of Mathematics, Ram Lal Anand College, University of Delhi, New Delhi, 110021, India

    Pooja Bansal

  2. Department of Mathematics, Jamia Millia Islamia, New Delhi, 110025, India

    Mohammad Hasan Shahid

  3. Department of Mathematics Education and RINS, Gyeongsang National University, Jinju, 52828, Republic of Korea

    Jae Won Lee

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  1. Pooja Bansal
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  2. Mohammad Hasan Shahid
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  3. Jae Won Lee
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Correspondence to Jae Won Lee.

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J. W. Lee was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government (MSIT) (2020R1F1A1A01069289)

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Bansal, P., Shahid, M.H. & Lee, J.W. \(\zeta \)-Ricci Soliton on Real Hypersurfaces of Nearly Kaehler 6-Sphere with SSMC. Mediterr. J. Math. 18, 93 (2021). https://doi.org/10.1007/s00009-021-01734-4

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  • DOI: https://doi.org/10.1007/s00009-021-01734-4

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