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A Note on Invariant Submanifolds of Trans-Sasakian Manifolds

Year 2016, Volume: 9 Issue: 2, 27 - 35, 30.10.2016
https://doi.org/10.36890/iejg.584576

Abstract

The object of this paper is to obtain some necessary and sufficient conditions for an invariant submanifold of a trans-Sasakian manifold to be totally geodesic. In addition, we construct an
example to verify our main results.

References

  • [1] Arslan, K., Lumiste, U., Murathn, C. and Özgür, C., 2-semiparallel surfaces in space forms, I: two particular cases, Proc. Est. Acad. Sci. Phys. Math. 49 (2000), no. 3, 139–148.
  • [2] Asperti, A. C., Lobos, G. A. and Mercuri, F., Pseudo-parallel immersions in space forms, Mat. Contemp. 17 (1999), 59–70.
  • [3] Blair, D. E. and Oubina, J. A., Conformal and related changes of metric on the product of two almost contact metric manifolds, Publ. Mat. 34 (1990), no. 1, 199–207.
  • [4] Chinea, D. and Prestelo, P. S., Invariant submanifolds of a trans-Sasakian manifold, Publ. Math. Debrecen 38 (1991), no, 1-2, 103–109.
  • [5] De, A., Totally geodesic submanifolds of a trans-Sasakian manifold, Proc. Est. Acad. Sci. 62 (2013), no. 4, 249–257.
  • [6] De, U. C. and Majhi, P., On invariant submanifolds of Kenmotsu manifolds, J. Geom. 106 (2015), no. 1, 109–122.
  • [7] Deprez, J., Semi-parallel surfaces in Euclidean space, J. Geom. 25 (1985), no. 2, 192–200.
  • [8] Deshmukh, S. and Tripathi, M. M., A note on trans-Sasakian manifolds, Math. Slovaca 63 (2013), no. 6, 1361–1370.
  • [9] Gray, A. and Hervella, L. M., The sixteen classes of almost Heritian manifolds and their linear invariants, Ann. Mat. Pura Appl. 123 (1980), no. 1, 35–58.
  • [10] Kobayashi, M., Semi-invariant submanifolds of a certain class of almost contact metric manifolds, Tensor (N.S.) 43 (1986), no. 1, 28–36.
  • [11] Kon, M., Invariant submanifols of normal contact metric manifolds, Kodai Math. Sem. Rep. 25 (1973), no. 3, 330–336.
  • [12] Kowalczyk, D., On some subclass of semisymmetric manifolds, Soochow J. Math. 27 (2001), no. 4, 445–462.
  • [13] Lotta, A., Slant submanifolds in contact geometry, Bull. Math. Soc. Roumanie 39 (1996), no. 1-4, 183–198.
  • [14] Mangione, V., Totally geodesic submanifolds of a Kenmotsu space form, Math. Reports 7 (2005), no. 4, 315–324.
  • [15] Murathan, C., Arslan, K. and Ezentas, E., Ricci generalized pseudo-symmetric immersions, Differ. Geom. Appl. 99–108, Matfyzpress, Prague, 2005.
  • [16] Oubina, J. A., New classes of almost contact metric structures, Publ. Math. Debrecen 32 (1985), no. 3-4, 187–193.
  • [17] Prasad, R. and Srivastava, V., Some results on trans-Sasakian manifofold, Mat. Vesnik. 65 (2013), no. 3, 346–352.
  • [18] Sarkar, A. and Sen, M., On invariant submanifolds of trans-Sasakian manifolds, Proc. Est. Acad. Sci. 61 (2012), no. 1, 29–37.
  • [19] Sular, S. and Özgür, C., On some submanifolds of Kenmotsu manifolds, Chaos Soliton Fract. 42 (2009), no. 4, 1990–1995.
  • [20] Vanli, A. T. and Sari, R., Invariant submanifolds of trans-Sasakian manifolds, Differ. Geom. Dyn. Syst. 12 (2010), 277–288.
  • [21] Verstraelen, L., Comments on pseudosymmetry in the sense of Ryszard Deszcz, Geometry and Topology of submanifolds, 6 (1994), no. 1,199–209.
Year 2016, Volume: 9 Issue: 2, 27 - 35, 30.10.2016
https://doi.org/10.36890/iejg.584576

Abstract

References

  • [1] Arslan, K., Lumiste, U., Murathn, C. and Özgür, C., 2-semiparallel surfaces in space forms, I: two particular cases, Proc. Est. Acad. Sci. Phys. Math. 49 (2000), no. 3, 139–148.
  • [2] Asperti, A. C., Lobos, G. A. and Mercuri, F., Pseudo-parallel immersions in space forms, Mat. Contemp. 17 (1999), 59–70.
  • [3] Blair, D. E. and Oubina, J. A., Conformal and related changes of metric on the product of two almost contact metric manifolds, Publ. Mat. 34 (1990), no. 1, 199–207.
  • [4] Chinea, D. and Prestelo, P. S., Invariant submanifolds of a trans-Sasakian manifold, Publ. Math. Debrecen 38 (1991), no, 1-2, 103–109.
  • [5] De, A., Totally geodesic submanifolds of a trans-Sasakian manifold, Proc. Est. Acad. Sci. 62 (2013), no. 4, 249–257.
  • [6] De, U. C. and Majhi, P., On invariant submanifolds of Kenmotsu manifolds, J. Geom. 106 (2015), no. 1, 109–122.
  • [7] Deprez, J., Semi-parallel surfaces in Euclidean space, J. Geom. 25 (1985), no. 2, 192–200.
  • [8] Deshmukh, S. and Tripathi, M. M., A note on trans-Sasakian manifolds, Math. Slovaca 63 (2013), no. 6, 1361–1370.
  • [9] Gray, A. and Hervella, L. M., The sixteen classes of almost Heritian manifolds and their linear invariants, Ann. Mat. Pura Appl. 123 (1980), no. 1, 35–58.
  • [10] Kobayashi, M., Semi-invariant submanifolds of a certain class of almost contact metric manifolds, Tensor (N.S.) 43 (1986), no. 1, 28–36.
  • [11] Kon, M., Invariant submanifols of normal contact metric manifolds, Kodai Math. Sem. Rep. 25 (1973), no. 3, 330–336.
  • [12] Kowalczyk, D., On some subclass of semisymmetric manifolds, Soochow J. Math. 27 (2001), no. 4, 445–462.
  • [13] Lotta, A., Slant submanifolds in contact geometry, Bull. Math. Soc. Roumanie 39 (1996), no. 1-4, 183–198.
  • [14] Mangione, V., Totally geodesic submanifolds of a Kenmotsu space form, Math. Reports 7 (2005), no. 4, 315–324.
  • [15] Murathan, C., Arslan, K. and Ezentas, E., Ricci generalized pseudo-symmetric immersions, Differ. Geom. Appl. 99–108, Matfyzpress, Prague, 2005.
  • [16] Oubina, J. A., New classes of almost contact metric structures, Publ. Math. Debrecen 32 (1985), no. 3-4, 187–193.
  • [17] Prasad, R. and Srivastava, V., Some results on trans-Sasakian manifofold, Mat. Vesnik. 65 (2013), no. 3, 346–352.
  • [18] Sarkar, A. and Sen, M., On invariant submanifolds of trans-Sasakian manifolds, Proc. Est. Acad. Sci. 61 (2012), no. 1, 29–37.
  • [19] Sular, S. and Özgür, C., On some submanifolds of Kenmotsu manifolds, Chaos Soliton Fract. 42 (2009), no. 4, 1990–1995.
  • [20] Vanli, A. T. and Sari, R., Invariant submanifolds of trans-Sasakian manifolds, Differ. Geom. Dyn. Syst. 12 (2010), 277–288.
  • [21] Verstraelen, L., Comments on pseudosymmetry in the sense of Ryszard Deszcz, Geometry and Topology of submanifolds, 6 (1994), no. 1,199–209.
There are 21 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Chaogui Hu This is me

Yaning Wang

Publication Date October 30, 2016
Published in Issue Year 2016 Volume: 9 Issue: 2

Cite

APA Hu, C., & Wang, Y. (2016). A Note on Invariant Submanifolds of Trans-Sasakian Manifolds. International Electronic Journal of Geometry, 9(2), 27-35. https://doi.org/10.36890/iejg.584576
AMA Hu C, Wang Y. A Note on Invariant Submanifolds of Trans-Sasakian Manifolds. Int. Electron. J. Geom. October 2016;9(2):27-35. doi:10.36890/iejg.584576
Chicago Hu, Chaogui, and Yaning Wang. “A Note on Invariant Submanifolds of Trans-Sasakian Manifolds”. International Electronic Journal of Geometry 9, no. 2 (October 2016): 27-35. https://doi.org/10.36890/iejg.584576.
EndNote Hu C, Wang Y (October 1, 2016) A Note on Invariant Submanifolds of Trans-Sasakian Manifolds. International Electronic Journal of Geometry 9 2 27–35.
IEEE C. Hu and Y. Wang, “A Note on Invariant Submanifolds of Trans-Sasakian Manifolds”, Int. Electron. J. Geom., vol. 9, no. 2, pp. 27–35, 2016, doi: 10.36890/iejg.584576.
ISNAD Hu, Chaogui - Wang, Yaning. “A Note on Invariant Submanifolds of Trans-Sasakian Manifolds”. International Electronic Journal of Geometry 9/2 (October 2016), 27-35. https://doi.org/10.36890/iejg.584576.
JAMA Hu C, Wang Y. A Note on Invariant Submanifolds of Trans-Sasakian Manifolds. Int. Electron. J. Geom. 2016;9:27–35.
MLA Hu, Chaogui and Yaning Wang. “A Note on Invariant Submanifolds of Trans-Sasakian Manifolds”. International Electronic Journal of Geometry, vol. 9, no. 2, 2016, pp. 27-35, doi:10.36890/iejg.584576.
Vancouver Hu C, Wang Y. A Note on Invariant Submanifolds of Trans-Sasakian Manifolds. Int. Electron. J. Geom. 2016;9(2):27-35.