Warped product submanifolds in generalized complex space forms

Mihai, Adela (2005) Warped product submanifolds in generalized complex space forms. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 21 (1). pp. 79-87. ISSN 0866-0174

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Abstract

B.Y. Chen established a sharp inequality for the warping func- tion of a warped product submanifold in a Riemannian space form in terms of the squared mean curvature. Later, in [4], 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 M1 ×f M2 in any generalized complex space form fM (c, α).

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