Contact 3-structure QR-warped product submanifold in Sasakian space form

372 99


In the present paper we obtain sharp estimates for the squared norm of the second fundamental form in terms of the mapping function for contact 3-structure CR-warped products isometrically immersed in Sasakian space form.


Warped product, contact QR-warped product, Sasakian space form

Full Text:



Barros, A., Chen, B. Y., Urbano, F.: Quaternion CR-submanifolds of a Quaternion Manifold, Kodai Math. J. 4, 399–418, (1981).

Bejancu, A.: Geometry of CR-submanifolds, D. Reidel Publishing Company, Dordrecht, Boston, Lancaster, Tokyo, (1986).

Bejancu, A.: CR-submanifolds of Ka¨ aler Manifold I , Proc. Amer. Math. Soc. 69, no.1, 135–142, (1978).

Blair, D. E., Chen, B. Y.: On CR-submanifolds of Hermitian Manifolds, Israel J. Math. 34, 353–363, (1979). Chen, B. Y.: Geometry of Warped Product CR-submanifolds of Ka¨ aler Manifolds, Monatsh. Math. 133, 177–195, (2001).

Kashiwada, T.: On a Contact 3-Structure, Math. Z. 238, 829–832, (2001).

Kenmotsu, K.: A Class of Almost Contact Riemannian Manifolds, Tohoku Math. J. 24, 93–103, (1972).

Kwon, J. H., Pak, J. S.: QR-submanifolds of (p − 1) QR-dimension in a Quaternionic Projective Space QP (n+p) 4 , Acta Math. Hungar. 86, 89–116, (2000).

Kuo, Y. Y., On Almost Contact 3 -Structure, Tˆ ohoku Math. J., 22, 325–332, (1970).

¨ Ozg¨ ur, C.: I On Weakly Symmetric Kenmotsu Manifolds, Differ. Geom. Dyn. Syst. 8, 204–206, (2006).

¨ Ozg¨ ur, C., De, U. C.: On the Quasi-Conformal Curvature Tensor of a Kenmotsu Manifold, Mathematica Pannonica. 17(2), 221–228, (2006).

Piti¸s, G.: A Remark on Kenmotsu Manifolds, Bull. Univ. Bra¸sov, Ser. C. 30, 31–32, (1988).

Yano, K., Kon, M.: Structure on Manifold, World Scientific, Singapore, (1984).