Contact CR-Warped Product Submanifolds in Sasakian Manifolds |
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| Authors: | Izumi Hasegawa Ion Mihai |
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| Institution: | (1) Department of Mathematics, Hokkaido University of Education, Ainosato, Kita-ku, Sapporo, 002-8502, Japan;(2) Faculty of Mathematics, University of Bucharest, Str. Academiei 14, 70109 Bucharest, Romania |
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| Abstract: | Recently, B.-Y. Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain a sharp inequality for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Sasakian manifolds. The equality case is considered. Also, the minimum codimension of a contact CR-warped product in an odd-dimensional sphere is determined. |
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| Keywords: | contact CR-submanifold Sasakian manifold Sasakian space form warped product |
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