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
[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.
[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.
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.