eesti teaduste
akadeemia kirjastus
SINCE 1952
Proceeding cover
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2022): 0.9
Totally geodesic submanifolds of a trans-Sasakian manifold; pp. 249–257
PDF | doi: 10.3176/proc.2013.4.05

Avik De

We consider invariant submanifolds of a trans-Sasakian manifold and obtain the conditions under which the submanifolds are totally geodesic. We also study invariant submanifolds of a trans-Sasakian manifold satisfying Z(XY).h = 0, where Z is the concircular curvature tensor.


  1. Aikawa, R. and Matsuyama, Y. On the local symmetry of Kaehler hypersurfaces. Yokohama Math. J., 2005, 51, 63–73.

  2. Blair, D. E. Riemannian Geometry of Contact and Symplectic Manifolds. Birkhäuser, Boston, 2002.

  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., 1990, 34, 199–207.

  4. Chen, B. Y. Geometry of Submanifolds. Marcel Dekker, New York, 1973.

  5. Chinea, D. and Prestelo, P. S. Invariant submanifolds of a trans-Sasakian manifold. Publ. Math. Debrecen, 1991, 38, 103–109.

  6. Deprez, J. Semi-parallel surfaces in Euclidean space. J. Geom., 1985, 25, 192–200.

  7. Deszcz, R. On pseudosymmetric spaces. Bull. Soc. Math. Belg. Ser. A., 1992, 44, 1–34.

  8. Gray, A. and Hervella, L. M. The sixteen classes of almost Hermitian manifolds and their linear invariants. Ann. Mat. Pura Appl. (4), 1980, 123, 35–58.

  9. Guojing, Z. and Jianguo, W. Invariant submanifolds and modes of non-linear autonomous systems. Appl. Math. Mech., 1998, 19, 587–693.

10. Janssens, D. and Vanheck, L. Almost contact structures and curvature tensors. Kodai Math. J., 1981, 4, 1–27.

11. Kobayashi, M. Semi-invariant submanifolds of a certain class of almost contact metric manifolds. Tensor (N.S.), 1986, 43, 28–36.

12. Kon, M. Invariant submanifolds of normal contact metric manifolds. Kodai Math. Sem. Rep., 1973, 27, 330–336.

13. Murathan, C., Arslan, K., and Ezentas, E. Ricci generalized pseudo-parallel immersions. In Differential Geometry and Its Applications: Proceedings, 9th International Conference on Differential Geometry and Its Applications, August 30–September 3, 2004, Prague, Czech Republic. Matfyzpress, Prague, 2005, 99–108.

14. Oubina, J. A. New classes of almost contact metric structures. Publ. Math. Debrecen, 1985, 32, 187–193.

15. Sarkar, A. and Sen, M. On invariant submanifolds of trans-Sasakian manifolds. Proc. Estonian Acad. Sci., 2012, 61, 29–37.

16. Sular, S. and Özgür, C. On some submanifolds of Kenmotsu manifolds. Chaos Soliton. Fract., 2009, 42, 1990–1995.

17. Vanli, A. T. and Sari, R. Invariant submanifolds of trans-Sasakian manifolds. DGDS, 2010, 12, 277–288.

18. Yano, K. and Kon, M. Structure on Manifolds. Series in Pure Mathematics. World Scientific Publishing, Singapore, 1984.

Back to Issue