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

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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

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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).