References

  1. Ahmad M., Jun J.B., Siddiqi M.D. On some properties of semi-invariant submanifolds of a nearly trans-Sasakian manifolds admitting a quarter-symmetric non-metric connection. J. Chungcheong Math. Soc. 2012, 25 (1), 73–80.
  2. Ahmad M., Rahman S., Siddiqi M.D. Semi-invariant submanifolds of a nearly Sasakian manifold endowed with a semi-symmetric metric connection. Bull. Allahabad Math. Soc. 2010, 25 (1), 23–33.
  3. Agashe N.S., Chafle M.R. A semi symmetric non-metric connection in a Riemannian manifold. Indian J. Pure Appl. Math. 1992, 23, 399–409.
  4. Cabrerizo J.L., Carriazo A., Fernández L.M., Fernández M. Structure on a slant submanifold of a contact manifold. Indian J. Pure Appl. Math. 2000, 31, 857–874.
  5. Chen B.-Y. Some pinching and classification theorems for mimimal submanifold. Arch. Math. 1993, 60 (6), 568–578. doi:10.1007/BF01236084
  6. Chen B.-Y. A Riemannian invariant and its applications to submanifold theory. Results Math. 1996, 27, 17–26. doi:10.1007/BF03322265
  7. Cioroboiu D., Oiaga A. B.Y. Chen inequalities for slant submanifolds in Sasakian space forms. Rend. Circ. Mat. Palermo (2) 2003, 52 (2), 367–381. doi:10.1007/BF02872761
  8. Defever F., Mihai I., Verstraelen L. B.-Y. Chen’s inequality for \(C\)-totally real submanifolds of Sasakian space forms. Boll. Unione Mat. Ital. 1997, 7 (11), 365–374.
  9. De U.C., De K. On a class of three-dimensional trans-Sasakian manifolds. Commun. Korean Math. Soc. 2012, 27 (4), 795–808.
  10. De U.C., Tripathi M.M. Ricci tensor in 3-dimensional trans-Sasakian manifolds. Kyungpook Math. J. 2003, 43, 247–255.
  11. De U.C., Kamilya D. Hypersurfaces of Rieamnnian manifold with semi-symmetric non-metric connection. J. Indian Inst. Sci. 1995, 75, 707–710.
  12. Golab S. On semi-symmetric and quarter-symmetric linear connections. Tensor (N.S.) 1975, 29, 249–254.
  13. Hayden H.A. Subspaces of a space with torsion. Proc. Lond. Math. Soc. (3) 1932, 34, 27–50. doi:10.1112/plms/s2-34.1.27
  14. Kim J.S., Prasad R., Tripathi M.M. On generalized Ricci-recurrent trans-Sasakian manifolds. J. Korean Math. Soc. 2002, 39 (6), 953–961. doi:10.4134/JKMS.2002.39.6.953
  15. Lotta A. Slant submanifolds in contact geometry. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 1996, 39 (87), 183–198.
  16. Marrero J.C. The local structure of trans-Sasakian manifolds. Ann. Mat. Pura Appl. (4) 1992, 162 (4), 77–86. doi:10.1007/BF01760000
  17. Mihai A., Ozgur C. Chen inequalities for submanifolds of real space forms with a semi-symmetric metric connection. Taiwanese J. Math. 2010, 14 (4), 1465–1477. doi:10.11650/twjm/1500405961
  18. Oubina J.A. New class of almost contact metric structures. Publ. Math. Debrecen 1985, 32, 187–193.
  19. Patra C., Bhattacharyya A. Trans-Sasakian manifold admitting quarter-symmetric non-metric connection. Acta Univ. Apulensis 2013, 36, 39–49.
  20. Sharfuddin A., Husain S.I. Semi-symmetric metric connections in almost contact manifolds. Tensor (N.S.) 1976, 30, 133–139.
  21. Siddiqui A.N., Murathan C., Siddiqi M.D. The Chen’s first inequality for submanifolds of statistical warped product manifolds. J. Geom. Phys. 2021, 169 (3), 104344. doi:10.1016/j.geomphys.2021.104344
  22. Siddiqui A.N., Chen B.-Y., Siddiqi M.D. Chen inequalities for statistical submersions between statistical manifolds. Int. J. Geom. Methods Mod. Phys. 2021, 18 (04), 2150049. doi:10.1142/S0219887821500493
  23. Tripathi M.M. A new connection in a Riemannian manifold. Int. Electron. J. Geom. 2008, 1 (1), 15–24.
  24. Yano K., Kon M. Structures on manifolds. In: Series in Pure Mathematics, 3. World Scientific Publ. Co., Singapore, 1984.