Abstract.
Our main theorem is a characterization of a totally geodesic Kähler immersion of a complex n-dimensional Kähler manifold M n into an arbitrary complex (n + p)-dimensional Kähler manifold \(\tilde{M}_{n+p}\) by observing the extrinsic shape of Kähler Frenet curves on the submanifold M n . Those curves are closely related to the complex structure of M n .
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Kim, Y., Maeda, S. A Practical Criterion For Some Submanifolds To Be Totally Geodesic. Mh Math 149, 233–242 (2006). https://doi.org/10.1007/s00605-005-0379-z
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DOI: https://doi.org/10.1007/s00605-005-0379-z