Warped Product Semi-Invariant Submanifolds in Almost Paracontact Riemannian Manifolds
We show that there exist no proper warped product semi-invariant submanifolds in almost paracontact Riemannian manifolds such that totally geodesic submanifold and totally umbilical submanifold of the warped product are invariant and anti-invariant, respectively. Therefore, we consider warped produc...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2009-01-01
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| Series: | Mathematical Problems in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2009/621625 |