Geodesic
Null 2-type Chen surfaces
Glasgow mathematical journal, Tome 37 (1995) no. 2, pp. 233-242

Voir la notice de l'article provenant de la source Cambridge University Press

Let M be an n-dimensional connected submanifold in an mdimensional Euclidean space Em. Denote by δ the Laplacian of M associated with the induced metric. Then the position vector x and the mean curvature vector H of Min Em satisfyThis yields the following fact: a submanifold M in Em is minimal if and only if all coordinate functions of Em, restricted to M, are harmonic functions. In other words, minimal submanifolds in Emare constructed from eigenfunctions of δ with one eigenvalue 0. By using (1. 1), T. Takahashi proved that minimal submanifolds of a hypersphere of Em are constructed from eigenfunctions of δ with one eigenvalue δ (≠0). In [3, 4], Chen initiated the study of submanifolds in Em which are constructed from harmonic functions and eigenfunctions of δ with a nonzero eigenvalue. The position vector x of such a submanifold admits the following simple spectral decomposition:for some non-constant maps x0and xq, where A is a nonzero constant. He simply calls such a submanifold a submanifold of null 2-type. 
Li, Shi-Jie. Null 2-type Chen surfaces. Glasgow mathematical journal, Tome 37 (1995) no. 2, pp. 233-242. doi: 10.1017/S001708950003113X
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