Variational characterizations of invariant submanifolds in Sasaki manifolds (Q6111111)

The paper deals with submanifolds tangent to the structure vector field in a Sasaki manifold. The main result is that for such a submanifold \(M\), the area functional is stationary if and only if \(M\) is an invariant submanifold. Provided the dimension of \(M\) is \(3\), the author proves that such a submanifold \(M\) is basic stable if and only if \(M\) is an invariant submanifold.