On semiparallel anti-invariant submanifolds of generalized Sasakian space forms

We consider minimal anti-invariant semiparallel submanifolds of generalized Sasakian space forms. We show that the submanifolds are totally geodesic under certain conditions.

On semiparallel anti-invariant submanifolds of generalized Sasakian space forms

We consider minimal anti-invariant semiparallel submanifolds of generalized Sasakian space forms. We show that the submanifolds are totally geodesic under certain conditions.

___

  • Alegre P, Blair DE, Carriazo A. Generalized Sasakian space-forms. Israel J Math 2004; 141: 157–183.
  • Alegre P, Carriazo A. Submanifolds of generalized Sasakian space forms. Taiwanese J Math 2009; 13: 923–941. Asperti AC, Mercuri F. Semi-parallel immersions into space forms. Boll Un Mat Ital 1994; 8B: 883–895.
  • Blair DE. Riemannian Geometry of Contact and Symplectic Manifolds. Boston: Birkhauser, 2002.
  • Brasil A, Lobos GA, Mariano M. C -totally real submanifolds with parallel mean curvature in λ -Sasakian space forms. Mat Contemp 2008; 34: 83–102.
  • Chen BY. Geometry of Submanifolds. Pure and Applied Mathematics. New York: Marcel Dekker, 1973.
  • Deprez J. Semiparallel hypersurfaces. Rend Sem Mat Univ Politec Torino 1986; 44: 303–316.
  • Deprez J. Semi-parallel immersions. In: Morvan JM, Verstraelen L, editors. Geometry and Topology of Submanifolds. Singapore: World Scientific, 1989, pp. 73–88.
  • Dillen F. Semi-parallel hypersurfaces of a real space form. Israel J Math 1991; 75: 193–202.
  • Janssens D, Vanhecke L. Almost contact structures and curvature tensors. Kodai Math J 1981; 4: 1–27.
  • Kenmotsu K. A class of almost contact Riemannian manifolds. Tohoku Math J 1972; 24: 93–103.
  • Ludden GD. Submanifolds of cosymplectic manifolds. J Differential Geometry 1970; 4: 237–244.
  • ¨ Ozg¨ ur C, Murathan C. On invariant submanifolds of Lorentzian para-Sasakian manifolds. Arab J Sci Eng Sect A Sci 2009; 34: 177–185.
  • Sular S. Kenmotsu manifolds and their some submanifolds. PhD, Balıkesir University, Balıkesir, Turkey, 2009. Sular S, ¨ Ozg¨ ur C, Murathan C. Pseudoparallel anti-invariant submanifolds of Kenmotsu manifolds. Hacettepe J Math Stat 2010; 39: 535–543.
  • Van der Veken J, Vrancken L. Parallel and semi-parallel hypersurfaces of S n × R. Bull Braz Math Soc (NS) 2008; 39: 355–370.
  • Yano K, Kon M. Structures on Manifolds. Series in Pure Mathematics. Singapore: World Scientific, 1984.
  • Yıldız A, Murathan C, Arslan K, Ezenta¸s R. C -totally real pseudo-parallel submanifolds of Sasakian space forms. Monatsh- Math 2007; 151: 247-256.