THE SMALLEST DİMENSİON SUBMANİFOLDS OF PARA B-KENMOTSU MANİFOLD

Abstract

In this paper, we study smallest dimensional submanifold of para Kenmotsu manifold. Necessary and sufficient conditions are given on a 3-dimensional submanifolds of 5-dimensional para Kenmotsu manifold to be slant submanifold. After, we study 3-dimensional minimal slant submanifolds of para Kenmotsu manifold. 

Keywords

• Para Kenmotsu manifold,smallest dimension,slant submanifold

The Smallest Dimension Submanifolds of Para 

Abstract

References

1. D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Progress in MathematicsVol. 203, Birkhauser, Boston, 2002.
2. J. L.Cabrerizo, A. Carriazo and L.M. Fernandez, Slant submanifolds in Sasakian manifolds. Glasgow Math. J. 42 (2000), 125-138.
3. A. Carriazo, New developments in slant submanifolds theory. In Applicable Mathematics in the Golden Age (2002), 339–356.
4. A. Carriazo, L.M. Fernandez and M.B. Hans-Uber, Minimal slant submanifolds of the smallest dimension in S-manifold, Rev.Mat. Iberoamericana 21 (2005), 47-66.
5. B.Y. Chen, Geometry of Slant Submanifolds, Katholieke Universiteit Leuven, 1990.
6. B.Y. Chen, Slant Immersions, Bull, Australian Math. Soc. 41 (1990), 135-147.
7. R.S. Gupta, and P.K. Pandey, Structure on a slant submanifold of a Kenmotsu manifold. Differential Geometry-Dynamical Systems 10 (2008), 139-147.
8. R.S. Gupta,S.M.K. Haider and M.H. Shaid, Slant submanifolds of Kenmotsu manifolds,Radovi Math., 12 (2004), 205-214.

9. A. Lotta, Slant submanifolds in contact geometry. Bull. Math. Soc. Roumanie. 39 (1996), 183-198.
10. A.Lotta, Three dimensional slant submanifolds of K-contact manifolds, Balkan J. Geom. Appl., 3 (1) (1998), 37-51.
11. I. Sato, On a structure similar to the almost contact structure, Tensor (N.S.), 30 (1976), 219-224.
12. Z. Olszak, The Schouten-Van Kampen Affine Connection Adapted to an Almost Para Contact Metric Structure, Pub. de Linst. Math., 94(108), (2013), 31-42.