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Lightlike Hypersurfaces of an Indefinite Kaehler Manifold with an $(\ell,\,m)$-type Metric Connection

Year 2023, , 526 - 538, 29.10.2023
https://doi.org/10.36890/iejg.1264249

Abstract

Jin introduced a non-symmetric metric connection, called an {\it $(\ell,m)$-type metric connection} \cite{Jin1, Jin2}.
There are two examples of $(\ell, m)$-type: a semi-symmetric metric connection when ${\ell}=1$ and $m=0$ and a quater-symmetric connection for ${\ell}=0$ and $m=1$ . Our purpose is to investigate lightlike hypersurfaces of an indefinite (complex) Kaehler manifolds with an $(\ell,m)$-type metric connection under the tangent characteristic vector field on such hypersurfaces.

References

  • [1] Anciaux, H., Panagiotidou, K.: Hopf hypersurfaces in pseudo-Riemannian complex and para-complex space forms. Diff. Geom. Appl. 42, 1-14 (2015).
  • [2] Duggal, K. L., Bejancu, A.: ightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Kluwer Acad. Publishers, Dordrecht (1996).
  • [3] De Rham, G.: Sur la r´eductibilit´e d’un espace de Riemannian. Comm. Math. Helv., 26, 328-344 (1952).
  • [4] Hayden, H. A.: Subspace of a space with torsion. Proc. London Math. Soc., 34, 27-50 (1932).
  • [5] Jin, D. H.: Lightlike hypersurfaces of an indefinite generalized Sasakian space form with a symmetric metric connection of type (ℓ,m). Commun.Korean Math. Soc., 31 (3), 613-624 (2016).
  • [6] Jin, D. H.: Lightlike hypersurfaces of an indefinite Kaehler manifold with a symmetric metric connection of type (ℓ,m). Bull. Korean Math. Soc., 53(4), 1171-1184 (2016).
  • [7] Jin, D. H.: Special lightlike hypersurfaces of indefinite Kaehler manifolds. Filomat. 30 (7), 1919-1930 (2016).
  • [8] Kimura, M., Ortega, M.: Hopf real hypersurfaces in the indefinite complex projective space. Mediterr. J. Math., 16:27 (2019).https://doi.org/10.1007/s00009-019-1299-9.
  • [9] Yano, K.: On semi-symmetric metric connections. Rev. Roumaine Math. Pures Appl., 15, 1579-1586 (1970).
  • [10] Yano, K., Imai, T.: Quarter-symmetric metric connection and their curvature tensors. Tensor, N.S., 38 (1982).
Year 2023, , 526 - 538, 29.10.2023
https://doi.org/10.36890/iejg.1264249

Abstract

References

  • [1] Anciaux, H., Panagiotidou, K.: Hopf hypersurfaces in pseudo-Riemannian complex and para-complex space forms. Diff. Geom. Appl. 42, 1-14 (2015).
  • [2] Duggal, K. L., Bejancu, A.: ightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Kluwer Acad. Publishers, Dordrecht (1996).
  • [3] De Rham, G.: Sur la r´eductibilit´e d’un espace de Riemannian. Comm. Math. Helv., 26, 328-344 (1952).
  • [4] Hayden, H. A.: Subspace of a space with torsion. Proc. London Math. Soc., 34, 27-50 (1932).
  • [5] Jin, D. H.: Lightlike hypersurfaces of an indefinite generalized Sasakian space form with a symmetric metric connection of type (ℓ,m). Commun.Korean Math. Soc., 31 (3), 613-624 (2016).
  • [6] Jin, D. H.: Lightlike hypersurfaces of an indefinite Kaehler manifold with a symmetric metric connection of type (ℓ,m). Bull. Korean Math. Soc., 53(4), 1171-1184 (2016).
  • [7] Jin, D. H.: Special lightlike hypersurfaces of indefinite Kaehler manifolds. Filomat. 30 (7), 1919-1930 (2016).
  • [8] Kimura, M., Ortega, M.: Hopf real hypersurfaces in the indefinite complex projective space. Mediterr. J. Math., 16:27 (2019).https://doi.org/10.1007/s00009-019-1299-9.
  • [9] Yano, K.: On semi-symmetric metric connections. Rev. Roumaine Math. Pures Appl., 15, 1579-1586 (1970).
  • [10] Yano, K., Imai, T.: Quarter-symmetric metric connection and their curvature tensors. Tensor, N.S., 38 (1982).
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Dae Ho Jin 0000-0002-7382-9333

Chul Woo Lee 0000-0003-0223-2318

Jae Won Lee 0000-0001-8562-0767

Early Pub Date October 15, 2023
Publication Date October 29, 2023
Acceptance Date September 11, 2023
Published in Issue Year 2023

Cite

APA Jin, D. H., Lee, C. W., & Lee, J. W. (2023). Lightlike Hypersurfaces of an Indefinite Kaehler Manifold with an $(\ell,\,m)$-type Metric Connection. International Electronic Journal of Geometry, 16(2), 526-538. https://doi.org/10.36890/iejg.1264249
AMA Jin DH, Lee CW, Lee JW. Lightlike Hypersurfaces of an Indefinite Kaehler Manifold with an $(\ell,\,m)$-type Metric Connection. Int. Electron. J. Geom. October 2023;16(2):526-538. doi:10.36890/iejg.1264249
Chicago Jin, Dae Ho, Chul Woo Lee, and Jae Won Lee. “Lightlike Hypersurfaces of an Indefinite Kaehler Manifold With an $(\ell,\,m)$-Type Metric Connection”. International Electronic Journal of Geometry 16, no. 2 (October 2023): 526-38. https://doi.org/10.36890/iejg.1264249.
EndNote Jin DH, Lee CW, Lee JW (October 1, 2023) Lightlike Hypersurfaces of an Indefinite Kaehler Manifold with an $(\ell,\,m)$-type Metric Connection. International Electronic Journal of Geometry 16 2 526–538.
IEEE D. H. Jin, C. W. Lee, and J. W. Lee, “Lightlike Hypersurfaces of an Indefinite Kaehler Manifold with an $(\ell,\,m)$-type Metric Connection”, Int. Electron. J. Geom., vol. 16, no. 2, pp. 526–538, 2023, doi: 10.36890/iejg.1264249.
ISNAD Jin, Dae Ho et al. “Lightlike Hypersurfaces of an Indefinite Kaehler Manifold With an $(\ell,\,m)$-Type Metric Connection”. International Electronic Journal of Geometry 16/2 (October 2023), 526-538. https://doi.org/10.36890/iejg.1264249.
JAMA Jin DH, Lee CW, Lee JW. Lightlike Hypersurfaces of an Indefinite Kaehler Manifold with an $(\ell,\,m)$-type Metric Connection. Int. Electron. J. Geom. 2023;16:526–538.
MLA Jin, Dae Ho et al. “Lightlike Hypersurfaces of an Indefinite Kaehler Manifold With an $(\ell,\,m)$-Type Metric Connection”. International Electronic Journal of Geometry, vol. 16, no. 2, 2023, pp. 526-38, doi:10.36890/iejg.1264249.
Vancouver Jin DH, Lee CW, Lee JW. Lightlike Hypersurfaces of an Indefinite Kaehler Manifold with an $(\ell,\,m)$-type Metric Connection. Int. Electron. J. Geom. 2023;16(2):526-38.