Anti-invariant submanifolds of a Kenmotsu manifold (Q2785898)

Let \(\overline{M}(\Phi, \xi, \eta,g)\) be an almost contact metric manifold. \(\overline M\) is a Kenmotsu manifold if NEWLINE\[NEWLINE(\overline\nabla_X\Phi)(Y) =g(\Phi X,Y) \xi- \eta(X) \Phi X, \quad \forall X,Y \in T\overline MNEWLINE\]NEWLINE [\textit{K. Kenmotsu}, Tôhoku Math. J. 24, 93-103 (1972; Zbl 0245.53040)]. An immersed submanifold \(M\) of \(\overline M\) is called anti-invariant if \(\Phi T_x M \subset T_x^\perp \overline M\) forall \(x\in M\).NEWLINENEWLINENEWLINEThe author establishes several properties of the geometric objects on such a manifold \(M\), when the vector field \(\xi\) is tangent to \(M\) and when \(\xi\) is normal to \(M\).