A Practical Criterion For Some Submanifolds To Be Totally Geodesic

Our main theorem is a characterization of a totally geodesic K?hler immersion of a complex n-dimensional K?hler manifold M _n into an arbitrary complex (n + p)-dimensional K?hler manifold (M)\tilde]_n+p\tilde{M}_{n+p} by observing the extrinsic shape of K?hler Frenet curves on the submanifold M _n . Those curves are closely related to the complex structure of M _n .