Characterizations of PR-Slant Warped Submanifolds in Para-Kaehler Spaces via Weingarten Maps

Source abstract

This paper investigates $\mathcal{P}\mathcal{R}$-pseudo-slant warped product submanifolds in para-K\"{a}hler manifolds $\bar{F}^{2m}$. First, fundamental properties of $\mathcal{P}\mathcal{R}$-pseudo-slant submanifolds in $\bar{F}^{2m}$ are obtained. Then non-existence and characterization results for $\mathcal{P}\mathcal{R}$-pseudo-slant warped product submanifolds are derived in terms of the Weingarten and endomorphism mappings, including the corresponding slant factor in $\bar{F}^{2m}$. In addition, a numerical example of the warped product $F_{\lambda}\times_{f}F_{\bot}$ in $\bar{F}^{2m}$ is provided to illustrate the results.