Abstract
In this paper, we initiate the study of ${\mathcal{P}} R$-warped products in para-Kähler manifolds and prove some fundamental results on such submanifolds. In particular, we establish a general optimal inequality for $\mathcal{P} R$-warped products in para-Kähler manifolds involving only the warping function and the second fundamental form. Moreover, we completely classify $\mathcal{P} R$-warped products in the flat para-Kähler manifold with least codimension which satisfy the equality case of the inequality. Our results provide an answer to the Open Problem (3) proposed in [19, Section 5].
Citation
Bang-Yen Chen. Marian Ioan Munteanu. "GEOMETRY OF ${\mathcal{P}} R$-WARPED PRODUCTS IN PARA-KÄHLER MANIFOLDS." Taiwanese J. Math. 16 (4) 1293 - 1327, 2012. https://doi.org/10.11650/twjm/1500406736
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