Semi-slant and bi-slant submanifolds of almost contact metric 3-structure manifolds

In this paper we introduce the notions of semi-slant and bi-slant submanifolds of an almost contact 3-structure manifold. We give some examples and characterization theorems about these submanifolds. Moreover, the distributions of semi-slant submanifolds of 3-cosymplectic and 3-Sasakian manifolds are studied.

Semi-slant and bi-slant submanifolds of almost contact metric 3-structure manifolds

In this paper we introduce the notions of semi-slant and bi-slant submanifolds of an almost contact 3-structure manifold. We give some examples and characterization theorems about these submanifolds. Moreover, the distributions of semi-slant submanifolds of 3-cosymplectic and 3-Sasakian manifolds are studied.

___

  • At¸ ceken, M.: Warped product semi-slant submanifolds in Kenmotsu manifolds. Turk. J. Math. 34, 325–432 (2010). Blair, D.E.: Riemannian geometry of contact and sympelectic manifolds. Boston-Basel-Berlin. Brikhauser 2002.
  • Cabrerizo, J.L., Carriazo, A., Fern´ andez, L.M., Fern´ andez, M.: Semi-slant submanifolds of a Sasakian manifold. Geom. Dedicata 78, 183–199 (1999).
  • Cabrerizo, J.L., Carriazo, A., Fern´ andez, L.M., Fern´ andez, M.: Slant submanifolds in Sasakian manifolds. Glasg. Math. J. 42, 125–138 (2000).
  • Carriazo, A.: Bi-slant immersions. Proc. ICRAMS 2000, Kharagpur, India, 88–97 (2000).
  • Chen, B.-Y.: Geometry of Slant Submanifolds. K.U. Leuven 1990.
  • Gibbons, G.W., Rychenkova, P.: Cones, tri-Sasakian structures and superconformal invariance. Phys. Lett. B 443, 138–142 (1998).
  • Kuo, Y.Y.: On almost contact 3-structure. T ´ o hoku Math. J. 22, 325–332 (1970).
  • Lotta, A.: Slant submanifolds in contact geometry. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 39, 183–198 (1996). Malek, F., Kazemi Balgeshir, M.B.: Slant submanifolds of almost contact metric 3-structure manifolds. Mediterr. J. Math., doi: 10.1007/s00009-012-0222-4.
  • Montano, B.C., De Nicola, A.: 3-Sasakian manifolds, 3-cosymplectic manifolds and Darboux theorem. J. Geom. Phys. 57, 2509–2520 (2007).
  • Papaghiuc, N.: Semi-slant submanifolds of a Kaehlerian manifold. An. Stiint. Al. I. Cuza. Univ. Iasi 40, 55–61 (1994).
  • Sahin, B.: Slant submanifolds of quaternion Kaehler manifolds. Commun. Korean Math. Soc. 22 (1), 123-135 (2007). Uddin, S., Khan, K.A.: Warped product semi-slant submanifolds of trans-Sasakian manifolds. Differ. Geom. Dyn. Syst. 12, 260–270 (2010).
  • Uddin, S., Khan, V.A., Khan, K.A.: Warped product submanifolds of a Kenmotsu manifold. Turk. J. Math. 36, 319–330 (2012).
  • Udriste, C.: Structures presque coquaternioniennes. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 13, 487–507 (1969).
  • Vˆılcu, G.E.: Slant submanifolds of quaternionic space forms. Publ. Math. Debrecen 81, 397–413 (2012).