UNIVERSITATIS APULENSIS No 10 / 2005 Proceedings of the International Conference on Theory and Application of Mathematics and Informatics ICTAMI 2005-Alba Iulia , Romania WARPED PRODUCT SUBMANIFOLDS IN QUATERNION SPACE FORMS (original) (raw)
B.Y. Chen [3] 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. For a survey on warped product submanifolds we refer to [4]. In [8], we established a similar relationship between the warping function f (intrinsic structure) and the squared mean curvature and the holomorphic sectional curvature (extrinsic structures) for warped product submanifolds M1 ×f M2 in any complex space form. In the present paper, we investigate warped product submanifolds in quaternion space forms M̃(4c). We obtain several estimates of the mean curvature in terms of the warping function, whether c < 0, c = 0 and c > 0, respectively. Equality cases are considered and certain examples are given. As applications, we derive obstructions to minimal warped product submanifolds in quaternion space forms. As an example, the non-existence of minimal proper warped product submanifolds M1 ×f M2 in the m-dimens...
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