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Zbl 1066.53103
Hasegawa, Izumi; Mihai, Ion
Contact CR-warped product submanifolds in Sasakian manifolds. (English)
[J] Geom. Dedicata 102, 143-150 (2003). ISSN 0046-5755; ISSN 1572-9168/e

Recently, B.-Y. Chen studied warped products which are CR-submanifolds in Kähler manifolds and established general sharp inequalities for CR-warped products in Kähler 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.
[Marcella Palese (Turin)]

MSC 2000:: *53C40 Submanifolds (differential geometry)

Keywords: contact CR-submanifold; Sasakian manifold; Sasakian space form; warped product

Cited in: Zbl 1224.53064 Zbl 1109.53056 Zbl 1114.53052 Zbl 1086.53078

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