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Semi-invariant warped product submanifolds of almost contact manifolds. (English) Zbl 1276.53063

Summary: In this article, we have obtained necessary and sufficient conditions in terms of the canonical structure \(F \) on a semi-invariant submanifold of an almost contact manifold under which the submanifold reduces to a semi-invariant warped product submanifold. Moreover, we have proved an inequality for the squared norm of the second fundamental form and finally, an estimate for the second fundamental form of a semi-invariant warped product submanifold in a generalized Sasakian space form is obtained, which extends the results of Chen, Al-Luhaibi et al., and Hesigawa and Mihai in a more general setting.

MSC:

53C40 Global submanifolds
53B25 Local submanifolds
53D15 Almost contact and almost symplectic manifolds
Full Text: DOI

References:

[1] doi:10.1007/s13348-010-0002-z · Zbl 1228.53036 · doi:10.1007/s13348-010-0002-z
[2] doi:10.1007/s006050170019 · Zbl 0996.53044 · doi:10.1007/s006050170019
[3] doi:10.1007/s10711-004-5459-z · Zbl 1114.53052 · doi:10.1007/s10711-004-5459-z
[4] doi:10.1007/BF01421206 · Zbl 0387.53014 · doi:10.1007/BF01421206
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