International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

Hyperbolic Kenmotsu Manifolds Admitting Schouten-Van Kampen Connection

  • Rajendra Prasad
  • Elsiddeg Ali
  • Mohammad Mahboob Alam
  • Abdul Haseeb*

    * Corresponding author

    Abstract

    In this paper we study certain curvature identities on hyperbolic Kenmotsu manifolds associated with the Schouten-Van Kampen connection. Also, we study hyperbolic Kenmotsu manifolds associated with the Schouten-Van Kampen connection that fulfills concircularly flat, ξ-concircularly flat, pseudo-concircularly flat, φ-concircularly flat, φ-concircularly semi-symmetric and Ricci semi-symmetric conditions. Moreover, we examine hyperbolic Kenmotsu manifolds with the Schouten-Van Kampen connection admitting Ricci solitons and η-Ricci solitons. To conclude, we present an illustration of a hyperbolic Kenmotsu manifold to validate certain results.

    How to Cite

    R. Prasad, E. Ali, M. M. Alam, A. Haseeb, Hyperbolic Kenmotsu Manifolds Admitting Schouten-Van Kampen Connection, Int. J. Anal. Appl. 24 (2026), 128. https://doi.org/10.28924/2291-8639-24-2026-128

    BibTeX
    @article{Prasad2026,
      author  = {Prasad, Rajendra and Ali, Elsiddeg and Alam, Mohammad Mahboob and Haseeb, Abdul},
      title   = {Hyperbolic Kenmotsu Manifolds Admitting Schouten-Van Kampen Connection},
      journal = {Int. J. Anal. Appl.},
      volume  = {24},
      year    = {2026},
      pages   = {128},
      doi     = {10.28924/2291-8639-24-2026-128}
    }

    References

    • [1] A.F. Solov'ev, On the Curvature of the Connection Induced on a Hyperdistribution in a Riemannian Space, Geom. Sb. 19 (1978), 12–23.
    • [2] G.P. Pokhariyal, R.S. Mishra, Curvature Tensor and Their Relativistic Significance, Yokohama Math. J. 18 (1970), 105–108.
    • [3] R. Prasad, V. Srivastava, ON $(\epsilon)$-Lorentzian Para-Sasakian MANIFOLDS, Commun. Korean Math. Soc. 27 (2012), 297–306. https://doi.org/10.4134/CKMS.2012.27.2.297.
    • [4] Z. Olszak, The Schouten-Van Kampen Affine Connection Adapted to an Almost (Para) Contact Metric Structure, Publ. Inst. Math. 94 (2013), 31–42. https://doi.org/10.2298/PIM1308031O.
    • [5] A. Bejancu, Schouten-van Kampen and Vranceanu Connections on Foliated Manifolds, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 52 (2006), 37–60.
    • [6] G. Ghosh, On Schouten-Van Kampen Connection in Sasakian Manifolds, Bol. Soc. Parana. Mat. 36 (2018), 171–182. https://doi.org/10.5269/bspm.v36i4.33105.
    • [7] A. Singh, C.K. Mishra, L. Kumar, S. Patel, Characterization of Kenmotsu Manifolds Admitting a Non-Symmetric Non-Metric Connection, J. Int. Acad. Phys. Sci. 26 (2022), 265–274.
    • [8] Y. Ramanaik, H.G. Nagaraja, Kenmotsu Manifold Admitting Shouten-van-Kampen Connection, Ann. Math. Comput. Sci. 12 (2023), 1–9.
    • [9] A. Yıldız, f-Kenmotsu Manifolds with the Schouten-Van Kampen Connection, Publ. Inst. Math. 102 (2017), 93–105. https://doi.org/10.2298/PIM1716093Y.
    • [10] A. Mondal, on f-Kenmotsu Manifolds Admitting Schouten-van Kampen Connection, Korean J. Math. 29 (2021), 333–344. https://doi.org/10.11568/kjm.2021.29.2.333.
    • [11] S. Zeren, A. Yildiz, S.Y. Perktas, Characterizations of Lorentzian Para-Sasakian Manifolds With Respect to the Schouten-Van Kampen Connection, Hagia Sophia J. Geom. 4 (2022), 1–10.
    • [12] P. Mandal, M.H. Shahid, S.K. Yadav, Conformal Ricci Soliton on Paracontact Metric $(k,\mu)$-Manifolds With Schouten-Van Kampen Connection, Commun. Korean Math. Soc. 39 (2024), 161–173. https://doi.org/10.4134/CKMS.c220099.
    • [13] A. Singh, L.S. Das, R. Prasad, L. Kumar, Some Properties of Kenmotsu Manifolds Admitting a New Type of Semi-Symmetric Non-Metric Connection, Commun. Math. Appl. 15 (2024), 145–160. https://doi.org/10.26713/cma.v15i1.2368.
    • [14] K. Kenmotsu, A Class of Almost Contact Riemannian Manifolds, Tohoku Math. J. 24 (1972), 93–103. https://doi.org/10.2748/tmj/1178241594.
    • [15] M.D. Upadhyay, K.K. Dube, Almost Contact Hyperbolic-$(\phi,\xi,\eta,\mathfrak{g})$ Structure, Acta Math. Acad. Sci. Hung. 28 (1976), 1–4. https://doi.org/10.1007/bf01902485.
    • [16] J. Das, A. Mandal, K. Halder, $\rho$-Yamabe Solitons on 3-Dimensional Hyperbolic Kenmotsu Manifolds, Int. J. Math. Comb. 2 (2024), 1–14.
    • [17] A. Singh, L.S. Das, P. Pankaj, S. Patel, Hyperbolic Kenmotsu Manifold Admitting a New Type of Semi-Symmetric Non-Metric Connection, Facta Univ. Ser.: Math. Inform. 39 (2024), 123–139. https://doi.org/10.22190/FUMI230207008S.
    • [18] A. Haseeb, R. Prasad, Certain Results on Lorentzian Para-Kenmotsu Manifolds, Bol. Soc. Parana. Mat. 39 (2021), 201–220. https://doi.org/10.5269/bspm.40607.
    • [19] Pankaj, S. K. Chaubey, G. Ayar, Yamabe and Gradient Yamabe Solitons on 3-Dimensional Hyperbolic Kenmotsu Manifolds, Differ. Geom. Dyn. Syst. 23 (2021), 175–188.
    • [20] M. Ahmad, K. Ali, CR-Submanifolds of a Nearly Hyperbolic Kenmotsu Manifold With Quarter Symmetric Non-Metric Connection, J. Math. Comput. Sci. 3 (2013), 905–917.
    • [21] K. Yano, Concircular Geometry I. Concircular Transformations, Proc. Jpn. Acad. Ser. A Math. Sci. 16 (1940), 195–200. https://doi.org/10.3792/pia/1195579139.
    • [22] A. Haseeb, R. Prasad, On Concircular Curvature Tensor in a Lorentzian $\alpha$-Sasakian Manifold with Respect to the Quarter-Symmetric Non-Metric Connection, Acta Comment. Univ. Tartu. Math. 22 (2019), 279–292. https://doi.org/10.12697/ACUTM.2018.22.23.
    • [23] S. Deshmukh, H. Alodan, H. Al-Sodais, A Note on Ricci Solitons, Balkan J. Geom. Appl. 16 (2011), 48–55.
    • [24] U. C. De, Ricci Soliton and Gradient Ricci Soliton on P-Sasakian Manifolds, Aligarh Bull. Math. 29 (2010), 29–34.
    • [25] A. Haseeb, R. Prasad, $\eta$-Ricci Solitons in Lorentzian $\alpha$-Sasakian Manifolds, Facta Univ. Ser.: Math. Inform. 35 (2020), 713–725. https://doi.org/10.22190/FUMI2003713H.
    • [26] A. Haseeb, R. Prasad, $\eta$-Ricci SOLITONS ON $\epsilon$-LP-Sasakian Manifolds with a Quarter-Symmetric METRIC CONNECTION, Honam Math. J. 41 (2019), 539–558. https://doi.org/10.5831/HMJ.2019.41.3.539.
    • [27] A. Kazan, H.B. Karadag, Trans-Sasakian Manifolds with Schouten-Van Kampen Connection, Ilirias J. Math. 7 (2018), 1–12.
    • [28] N.G. Halammanavar, K.K.L. Devasandra, Kenmotsu Manifolds Admitting Schouten-Van Kampen Connection, Facta Univ. Ser.: Math. Inform. 34 (2019), 23–34. https://doi.org/10.22190/FUMI1901023H.