A Note on Invariant Submanifolds of Trans-Sasakian Manifolds Chaogui Hu and Yaning Wang* (Communicated by Levent Kula)

A Note on Invariant Submanifolds of Trans-Sasakian Manifolds Chaogui Hu and Yaning Wang* (Communicated by Levent Kula)

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

___

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