Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 21, No. 1, pp. 79-87 (2005)

Warped product submanifolds in generalized complex space forms

Adela Mihai

University of Bucharest

Abstract: B.Y. Chen established a sharp inequality for the warping function of a warped product submanifold in a Riemannian space form in terms of the squared mean curvature. Later he studied warped product submanifolds in complex hyperbolic spaces.

In the present paper, we establish an inequality between the warping function $f$ (intrinsic structure) and the squared mean curvature $\|H\|^2$ and the holomorphic sectional curvature $c$ (extrinsic structures) for warped product submanifolds $M_1\times_fM_2$ in any generalized complex space form $\widetilde M(c,\alpha)$.

Keywords: Generalized complex space forms, warped products, CR-warped products, CR-products, warping function.

Classification (MSC2000): 53C40; 53C15, 53C42

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