Research Article
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Year 2023, , 349 - 357, 30.04.2023
https://doi.org/10.36890/iejg.1200729

Abstract

References

  • [1] Adati, T., Miiyazawa.: On P-Sasakian manifolds satisfying certain conditions. Tensor(N.S) 33, 173-178 (1979).
  • [2] Bejancu, A., Faran, H.: Foliations and Geometric Structures. Dordrecht, Netherlands, (2006).
  • [3] Bejancu, A.: Schouten-van Kampen and Vranceanu connections on Foliated manifolds Anal. Univ.(Al.I.Cuza’Iasi Mat.) 52, 37-60 (2006).
  • [4] Ghosh, G.: On Schouten-van Kampen connection on Sasakian manifolds Bo-letim da Sociedade Paranaense de Matematica. 36, 171-182 (2018).
  • [5] Ianus, S.: Some almost product structures on manifolds with the linear connection Kodai Mathematical Seminar Reports. 23, 305-310 (1971).
  • [6] Kuhnel, W.: Conformal transformations between Einstein spaces. Aspects Math. E12, Friedr. Vieweg, Braunschweing, 1988.
  • [7] Mandal, K., De, U.C.: Quarter-symmetric metric connection in a P-Sasakian manifold, Annals of West University of Timisoara-Mathematics and Computer Science. 53 (1), 137-150 (2015).
  • [8] Matsumoto, K., Ianus, S., Mihai, I.: On P-Sasakian manifolds which admit certain tensor-fields Publicationes Mathematicae-Debrecen. 33, 199-205 (1986).
  • [9] Mondal, A.: On f-Kenmotsu manifolds admitting Schouten-Van Kampen connection The Korean Journal of Mathematics, Gorakhpur. 29 (2), 333-344 (2021).
  • [10] Nagaraja, H. G., Kumar, D.L.K.: Kenmotsu manifolds admitting Schouten-van Kampen Connection Facta Universitatis, Series: Mathematics and Informatics. 34, 23-34 (2019).
  • [11] Olszak, Z.: The Schouten–van Kampen affine connection adapted an almost (para) contact metric structure . Publications de l’Institut Mathematique. 94, 31-42 (2013).
  • [12] Olszak, Z., Rosca, R.: Normal locally conformal almost cosymplectic manifolds Publicationes Mathematicae Debrecen. 39, 315-323 (1991).
  • [13] Ozgur, C., On A class of para-Sakakian manifolds Turkish Journal of Mathematics. 29(3), 249-258 (2005).
  • [14] Perktas, Y.S., Yildiz, A.: On Quasi-Sasakian 3-Manifolds with Respect to the Schouten-van Kampen Connection International Electronic Journal of Geometry. 13 (2), 62-74 (2020).
  • [15] Perktas, Y.S., Yildiz, A.: On f-Kenmotsu 3-manifolds with respect to the Schouten-van Kampen connection Turkish J. of Math. 45, 387-409 (2021).
  • [16] Sasaki, S., Hatakeyama, Y.: On differentiable manifolds with certain structures which are closely related to almost contact structures II Tohoku Mathematical Journal, 13, 281-294 (1961).
  • [17] Sato, I.: On a structure similar to the almost contact structure Tensor(N.S). 30, 219-224 (1976).
  • [18] Sato, I., Matsumoto, K.: On P-Sahakian manifolds satisfying certain conditions Tensor(N.S). 33, 173-178 (1979).
  • [19] Schouten, J., van Kampen, E.: Zur Einbettungs-und Krummungsthorie nichtholonomer Gebilde Mathematische Annalen. 103, 752-783 (1930).
  • [20] Shukla, S. S., Shukla, M. K.: On ϕ-symmetric Para-Sasakian manifolds Int. J. Math. Analysis, 16 (4), 761-769 (2010).
  • [21] Solov’ev, A. F.: On the curvature of the connection induced on a hyperdistribution in a Riemannian space Geometricheskii Sbornik. 19, 12-23 (1978).
  • [22] Solov’ev, A. F.: The bending of hyperdistributions Geometricheskii Sbornik. 20, 101-112 (1979).
  • [23] Solov’ev, A. F.: Second fundamental form of a distribution Matematicheskie Zametki. 35, 139-146 (1982).
  • [24] Solov’ev, A. F.: Curvature of a distribution Matematicheskie Zametki. 35, 111-124 (1984).
  • [25] Yano, K.: Concircular geometry I. concircular transformations Proc. Inst. Acad. Tokyo. 16, 195-200 (1940).
  • [26] Yano, K., Bochner, S.: Curvature and Betti numbers. Annals of Math. Studies 32, Princeton university press, 1953.
  • [27] Yano, K., Kon, M.: Structures on manifolds, Series in Pure Mathematics, 3. World Scientific, 1984.
  • [28] Yıldız, A.: f-Kenmotsu manifolds with the Schouten–van Kampen connection Publications de l’Institut Mathematique. 102 (116), 93-105 (2017).
  • [29] Yıldız, A., Turan, M., Acet, B. E.: On Para-Sasakian manifolds Journal of Science and Technology of Dumlupınar University. 24, 27-34 (2011).

On Para-Sasakian Manifold with Respect to the Schouten-van Kampen Connection

Year 2023, , 349 - 357, 30.04.2023
https://doi.org/10.36890/iejg.1200729

Abstract

In the present paper, we have studied the curvature properties of the Schouten-van Kampen
connection on the n-dimensional Para Sasakian manifold and obtained some new results. Also,
we studied projective curvature tensor, concircular curvature tensor, and Nijenhuis tensor for the
Para-Sasakian manifold with respect to the Schouten-van Kampen connection.

References

  • [1] Adati, T., Miiyazawa.: On P-Sasakian manifolds satisfying certain conditions. Tensor(N.S) 33, 173-178 (1979).
  • [2] Bejancu, A., Faran, H.: Foliations and Geometric Structures. Dordrecht, Netherlands, (2006).
  • [3] Bejancu, A.: Schouten-van Kampen and Vranceanu connections on Foliated manifolds Anal. Univ.(Al.I.Cuza’Iasi Mat.) 52, 37-60 (2006).
  • [4] Ghosh, G.: On Schouten-van Kampen connection on Sasakian manifolds Bo-letim da Sociedade Paranaense de Matematica. 36, 171-182 (2018).
  • [5] Ianus, S.: Some almost product structures on manifolds with the linear connection Kodai Mathematical Seminar Reports. 23, 305-310 (1971).
  • [6] Kuhnel, W.: Conformal transformations between Einstein spaces. Aspects Math. E12, Friedr. Vieweg, Braunschweing, 1988.
  • [7] Mandal, K., De, U.C.: Quarter-symmetric metric connection in a P-Sasakian manifold, Annals of West University of Timisoara-Mathematics and Computer Science. 53 (1), 137-150 (2015).
  • [8] Matsumoto, K., Ianus, S., Mihai, I.: On P-Sasakian manifolds which admit certain tensor-fields Publicationes Mathematicae-Debrecen. 33, 199-205 (1986).
  • [9] Mondal, A.: On f-Kenmotsu manifolds admitting Schouten-Van Kampen connection The Korean Journal of Mathematics, Gorakhpur. 29 (2), 333-344 (2021).
  • [10] Nagaraja, H. G., Kumar, D.L.K.: Kenmotsu manifolds admitting Schouten-van Kampen Connection Facta Universitatis, Series: Mathematics and Informatics. 34, 23-34 (2019).
  • [11] Olszak, Z.: The Schouten–van Kampen affine connection adapted an almost (para) contact metric structure . Publications de l’Institut Mathematique. 94, 31-42 (2013).
  • [12] Olszak, Z., Rosca, R.: Normal locally conformal almost cosymplectic manifolds Publicationes Mathematicae Debrecen. 39, 315-323 (1991).
  • [13] Ozgur, C., On A class of para-Sakakian manifolds Turkish Journal of Mathematics. 29(3), 249-258 (2005).
  • [14] Perktas, Y.S., Yildiz, A.: On Quasi-Sasakian 3-Manifolds with Respect to the Schouten-van Kampen Connection International Electronic Journal of Geometry. 13 (2), 62-74 (2020).
  • [15] Perktas, Y.S., Yildiz, A.: On f-Kenmotsu 3-manifolds with respect to the Schouten-van Kampen connection Turkish J. of Math. 45, 387-409 (2021).
  • [16] Sasaki, S., Hatakeyama, Y.: On differentiable manifolds with certain structures which are closely related to almost contact structures II Tohoku Mathematical Journal, 13, 281-294 (1961).
  • [17] Sato, I.: On a structure similar to the almost contact structure Tensor(N.S). 30, 219-224 (1976).
  • [18] Sato, I., Matsumoto, K.: On P-Sahakian manifolds satisfying certain conditions Tensor(N.S). 33, 173-178 (1979).
  • [19] Schouten, J., van Kampen, E.: Zur Einbettungs-und Krummungsthorie nichtholonomer Gebilde Mathematische Annalen. 103, 752-783 (1930).
  • [20] Shukla, S. S., Shukla, M. K.: On ϕ-symmetric Para-Sasakian manifolds Int. J. Math. Analysis, 16 (4), 761-769 (2010).
  • [21] Solov’ev, A. F.: On the curvature of the connection induced on a hyperdistribution in a Riemannian space Geometricheskii Sbornik. 19, 12-23 (1978).
  • [22] Solov’ev, A. F.: The bending of hyperdistributions Geometricheskii Sbornik. 20, 101-112 (1979).
  • [23] Solov’ev, A. F.: Second fundamental form of a distribution Matematicheskie Zametki. 35, 139-146 (1982).
  • [24] Solov’ev, A. F.: Curvature of a distribution Matematicheskie Zametki. 35, 111-124 (1984).
  • [25] Yano, K.: Concircular geometry I. concircular transformations Proc. Inst. Acad. Tokyo. 16, 195-200 (1940).
  • [26] Yano, K., Bochner, S.: Curvature and Betti numbers. Annals of Math. Studies 32, Princeton university press, 1953.
  • [27] Yano, K., Kon, M.: Structures on manifolds, Series in Pure Mathematics, 3. World Scientific, 1984.
  • [28] Yıldız, A.: f-Kenmotsu manifolds with the Schouten–van Kampen connection Publications de l’Institut Mathematique. 102 (116), 93-105 (2017).
  • [29] Yıldız, A., Turan, M., Acet, B. E.: On Para-Sasakian manifolds Journal of Science and Technology of Dumlupınar University. 24, 27-34 (2011).
There are 29 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Shivani Sundriyal 0000-0001-6195-2572

Jaya Upreti 0000-0001-8615-1819

Publication Date April 30, 2023
Acceptance Date April 1, 2023
Published in Issue Year 2023

Cite

APA Sundriyal, S., & Upreti, J. (2023). On Para-Sasakian Manifold with Respect to the Schouten-van Kampen Connection. International Electronic Journal of Geometry, 16(1), 349-357. https://doi.org/10.36890/iejg.1200729
AMA Sundriyal S, Upreti J. On Para-Sasakian Manifold with Respect to the Schouten-van Kampen Connection. Int. Electron. J. Geom. April 2023;16(1):349-357. doi:10.36890/iejg.1200729
Chicago Sundriyal, Shivani, and Jaya Upreti. “On Para-Sasakian Manifold With Respect to the Schouten-Van Kampen Connection”. International Electronic Journal of Geometry 16, no. 1 (April 2023): 349-57. https://doi.org/10.36890/iejg.1200729.
EndNote Sundriyal S, Upreti J (April 1, 2023) On Para-Sasakian Manifold with Respect to the Schouten-van Kampen Connection. International Electronic Journal of Geometry 16 1 349–357.
IEEE S. Sundriyal and J. Upreti, “On Para-Sasakian Manifold with Respect to the Schouten-van Kampen Connection”, Int. Electron. J. Geom., vol. 16, no. 1, pp. 349–357, 2023, doi: 10.36890/iejg.1200729.
ISNAD Sundriyal, Shivani - Upreti, Jaya. “On Para-Sasakian Manifold With Respect to the Schouten-Van Kampen Connection”. International Electronic Journal of Geometry 16/1 (April 2023), 349-357. https://doi.org/10.36890/iejg.1200729.
JAMA Sundriyal S, Upreti J. On Para-Sasakian Manifold with Respect to the Schouten-van Kampen Connection. Int. Electron. J. Geom. 2023;16:349–357.
MLA Sundriyal, Shivani and Jaya Upreti. “On Para-Sasakian Manifold With Respect to the Schouten-Van Kampen Connection”. International Electronic Journal of Geometry, vol. 16, no. 1, 2023, pp. 349-57, doi:10.36890/iejg.1200729.
Vancouver Sundriyal S, Upreti J. On Para-Sasakian Manifold with Respect to the Schouten-van Kampen Connection. Int. Electron. J. Geom. 2023;16(1):349-57.