On invariant submanifolds of contact metric manifolds (Q5896617)

The author generalizes two results by \textit{M. Kon} [Kodai Math. J. 25, 330-336 (1973; Zbl 0265.53049)]. Firstly, if \(M^{2n+1}\) is an invariant submanifold of a contact metric manifold \(\bar M\) of pointwise constant \({\bar \phi}\)-sectional curvature \(\bar K,\) then the scalar curvature S of M satisfies \(S\leq n^ 2(\bar K+3)+n(\bar K+1).\) Secondly, if there exists an invariant Einstein submanifold M in a K-contact Riemannian manifold \(\bar M\) of pointwise constant \({\bar \phi}\)-sectional curvature \(\bar K,\) then \(\bar K\geq 1\). In both results equality holds if and only if M is totally geodesic and Sasakian.