## Integral submanifolds in three-Sasakian manifolds whose mean curvature vector fields are eigenvectors of the Laplace operator.(English)Zbl 1192.53050

Mladenov, Ivaïlo M. (ed.), Proceedings of the 9th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 8–13, 2007. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-42-4/pbk). 210-223 (2008).
Summary: We find the Legendre curves and a class of integral surfaces in a 7-dimensional three-Sasakian manifold whose mean curvature vectors are eigenvectors of the Laplacian or the normal Laplacian, and, we give the explicit expression for such surfaces in the sphere $$\mathbb S^7$$.
For the entire collection see [Zbl 1154.17001].

### MSC:

 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions 53C40 Global submanifolds

### Keywords:

normal Laplacian; harmonic mean curvature vector field