Optimal inequalities for the normalized \(\delta\)-Casorati curvatures of submanifolds in Kenmotsu space forms
An almost contact manifold \(\bar{M}\) is said to be \textit{Kenmotsu} whenever the structure tensors \((\phi, \xi, \eta)\) satify certain natural equations involving the Levi-Civita connection \(\bar\nabla\) of the Riemannian metric \(\bar{g}\) of \(\bar{M}\); such an \(\bar{M}\) is a \textit{Kenmotsu space form} whenever its sectional curvatures are the same along all \(\phi\)-holomorphic planes. \textit{Casorati curvatures} of submanifolds of Riemannian spaces are certain scalar quantities expressed in terms of their second fundamental forms. Here, the authors provide certain upper estimates of Casorati curvatures for submanifolds \(M\) of Kenmotsu space forms \(\bar{M}\) provided that \(\dim M = m+1\), \(\dim\bar{M} = 2m+1\) and \(\xi\in TM\).
almost contact manifold, Kenmotsu space form
scientific article; zbMATH DE number 6854802
scientific article