Research Article
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Year 2024, , 394 - 401, 27.10.2024
https://doi.org/10.36890/iejg.1470495

Abstract

References

  • [1] Blair D. E., On the geometric meaning of the Bochner Tensor, Geom. Dedicata 4, 33-38 (1975).
  • [2] Blair D.E., Koufogiorgos T., Papantoniou B. J., Contact metric manifolds satisfying a nullity condition, Israel Journal of Math. 91, 189-214 (1995).
  • [3] Blair D.E., Two remarks on contact metric structures, Tôhoku Math. J., 29, 319-324, (1977).
  • [4] Bochner S., Curvature and Betti numbers, Ann. of Math. (2) 50, 77-93 (1949).
  • [5] Boothby W. M., and Wang H. C., On contact manifolds, Ann. of Math. 68, 721-734 (1958).
  • [6] Endo H., On K-contact Riemannian manifolds with vanishing E-contact Bochner curvature tensor, Colloq. Math., Vol.LXII, no.2, 293-297 (1991).
  • [7] Hasegawa I. and Nakane T., On Sasakian manifolds with vanishing contact Bochner curvature tensor II, Hokkaido Math. J. 11 , 44-51 (1982).
  • [8] Ikawa T. and Kon M., Sasakian manifolds with vanishing contact Bochner curvature tensor and constant scalar curvature, Colloq. Math. 37, 113-122 (1977).
  • [9] Matsumoto M. and Chuman G., On the C-Bochner curvature tensor, TRU Math., 5 , 21-30 (1969).
  • [10] Papantoniou B. J., Contact Riemannian manifolds satisfying R(ξ,X) · R = 0 and ξ ∈ (`k,`μ)-nullity distribution, Yokohama Math. J., 40, 149-161 (1993).
  • [11] Shaikh A. A. and Baishya, K. K., On (`k,`μ)-contact metric manifolds, Diff. Geom.-Dynm. System, 8 , 253-261 (2006).
  • [12] Yano K., Differential geometry of anti-invariant submanifolds of a Sasakian manifold, Boll. Un. Mat. Ital., 12 , 279-296 (1975).
  • [13] Yano K., Anti-invariant submanifolds of a Sasakian manifold with vanishing contact Bochner curvature tensor, J. Diff. Geom., 12 , 153-170 (1977).

Generalized Extended $C$-Bochner Curvature Tensor on $(\grave{k},\grave{\mu})$-Contact Metric Manifolds

Year 2024, , 394 - 401, 27.10.2024
https://doi.org/10.36890/iejg.1470495

Abstract

The object of the present paper is to study $(\grave{k},\grave{\mu})$-contact metric manifolds with generalized extended $C$-Bochner curvature tensor.

References

  • [1] Blair D. E., On the geometric meaning of the Bochner Tensor, Geom. Dedicata 4, 33-38 (1975).
  • [2] Blair D.E., Koufogiorgos T., Papantoniou B. J., Contact metric manifolds satisfying a nullity condition, Israel Journal of Math. 91, 189-214 (1995).
  • [3] Blair D.E., Two remarks on contact metric structures, Tôhoku Math. J., 29, 319-324, (1977).
  • [4] Bochner S., Curvature and Betti numbers, Ann. of Math. (2) 50, 77-93 (1949).
  • [5] Boothby W. M., and Wang H. C., On contact manifolds, Ann. of Math. 68, 721-734 (1958).
  • [6] Endo H., On K-contact Riemannian manifolds with vanishing E-contact Bochner curvature tensor, Colloq. Math., Vol.LXII, no.2, 293-297 (1991).
  • [7] Hasegawa I. and Nakane T., On Sasakian manifolds with vanishing contact Bochner curvature tensor II, Hokkaido Math. J. 11 , 44-51 (1982).
  • [8] Ikawa T. and Kon M., Sasakian manifolds with vanishing contact Bochner curvature tensor and constant scalar curvature, Colloq. Math. 37, 113-122 (1977).
  • [9] Matsumoto M. and Chuman G., On the C-Bochner curvature tensor, TRU Math., 5 , 21-30 (1969).
  • [10] Papantoniou B. J., Contact Riemannian manifolds satisfying R(ξ,X) · R = 0 and ξ ∈ (`k,`μ)-nullity distribution, Yokohama Math. J., 40, 149-161 (1993).
  • [11] Shaikh A. A. and Baishya, K. K., On (`k,`μ)-contact metric manifolds, Diff. Geom.-Dynm. System, 8 , 253-261 (2006).
  • [12] Yano K., Differential geometry of anti-invariant submanifolds of a Sasakian manifold, Boll. Un. Mat. Ital., 12 , 279-296 (1975).
  • [13] Yano K., Anti-invariant submanifolds of a Sasakian manifold with vanishing contact Bochner curvature tensor, J. Diff. Geom., 12 , 153-170 (1977).
There are 13 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Article
Authors

Ahmet Yıldız 0000-0002-9799-1781

Early Pub Date September 19, 2024
Publication Date October 27, 2024
Submission Date April 18, 2024
Acceptance Date July 11, 2024
Published in Issue Year 2024

Cite

APA Yıldız, A. (2024). Generalized Extended $C$-Bochner Curvature Tensor on $(\grave{k},\grave{\mu})$-Contact Metric Manifolds. International Electronic Journal of Geometry, 17(2), 394-401. https://doi.org/10.36890/iejg.1470495
AMA Yıldız A. Generalized Extended $C$-Bochner Curvature Tensor on $(\grave{k},\grave{\mu})$-Contact Metric Manifolds. Int. Electron. J. Geom. October 2024;17(2):394-401. doi:10.36890/iejg.1470495
Chicago Yıldız, Ahmet. “Generalized Extended $C$-Bochner Curvature Tensor on $(\grave{k},\grave{\mu})$-Contact Metric Manifolds”. International Electronic Journal of Geometry 17, no. 2 (October 2024): 394-401. https://doi.org/10.36890/iejg.1470495.
EndNote Yıldız A (October 1, 2024) Generalized Extended $C$-Bochner Curvature Tensor on $(\grave{k},\grave{\mu})$-Contact Metric Manifolds. International Electronic Journal of Geometry 17 2 394–401.
IEEE A. Yıldız, “Generalized Extended $C$-Bochner Curvature Tensor on $(\grave{k},\grave{\mu})$-Contact Metric Manifolds”, Int. Electron. J. Geom., vol. 17, no. 2, pp. 394–401, 2024, doi: 10.36890/iejg.1470495.
ISNAD Yıldız, Ahmet. “Generalized Extended $C$-Bochner Curvature Tensor on $(\grave{k},\grave{\mu})$-Contact Metric Manifolds”. International Electronic Journal of Geometry 17/2 (October 2024), 394-401. https://doi.org/10.36890/iejg.1470495.
JAMA Yıldız A. Generalized Extended $C$-Bochner Curvature Tensor on $(\grave{k},\grave{\mu})$-Contact Metric Manifolds. Int. Electron. J. Geom. 2024;17:394–401.
MLA Yıldız, Ahmet. “Generalized Extended $C$-Bochner Curvature Tensor on $(\grave{k},\grave{\mu})$-Contact Metric Manifolds”. International Electronic Journal of Geometry, vol. 17, no. 2, 2024, pp. 394-01, doi:10.36890/iejg.1470495.
Vancouver Yıldız A. Generalized Extended $C$-Bochner Curvature Tensor on $(\grave{k},\grave{\mu})$-Contact Metric Manifolds. Int. Electron. J. Geom. 2024;17(2):394-401.