Geometric classification of warped product submanifolds of nearly Kaehler manifolds with a slant fiber

다국어 초록 (Multilingual Abstract)

<P>There are two types of warped product pseudo-slant submanifolds, <TEX>$ M_{\theta } \times _{f}M_{\bot }$</TEX> and <TEX>$ M_{\bot }\times _{f}M_{\theta }$</TEX>, in a nearly Kaehler manifold. We derive an optimization for an extrinsic invariant, the squared norm of second fundamental form, on a nontrivial warped product pseudo-slant submanifold <TEX>$ M_{\bot }\times _{f}M_{\theta }$</TEX> in a nearly Kaehler manifold in terms of a warping function and a slant angle when the fiber <TEX>$ M_{\theta }$</TEX> is a slant submanifold. Moreover, the equality is verified for depending on what <TEX>$ M_{\theta }$</TEX> and <TEX>$ M_{\bot }$</TEX> are, and also we show that if the equality holds, then <TEX>$ M_{\bot }\times _{f}M_{\theta }$</TEX> is a simply Riemannian product. As applications, we prove that the warped product pseudo-slant submanifold has the finite Kinetic energy if and only if <TEX>$ M_{\bot }\times _{f}M_{\theta }$</TEX> is a totally real warped product submanifold.</P>