Biwarped product submanifolds of a Kähler manifold. (English) Zbl 1499.53306
Summary: We study biwarped product submanifolds which are special cases of multiply warped product submanifolds in Kähler manifolds. We observe the non-existence of such submanifolds under some circumstances. We show that there exists a non-trivial biwarped product submanifold of a certain type by giving an illustrate example. We also give a necessary and sufficient condition for such submanifolds to be locally trivial. Moreover, we establish an inequality for the squared norm of the second fundamental form in terms of the warping functions for such submanifolds. The equality case is also discussed.
MSC:
| 53C55 | Global differential geometry of Hermitian and Kählerian manifolds |
| 53B25 | Local submanifolds |
| 53C40 | Global submanifolds |
Keywords:
warped product; multiply warped product; holomorphic distribution; totally real submanifold; pointwise slant distribution; Kähler manifoldReferences:
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