Abstract
We classify constant Gaussian curvature surfaces with nonzero parallel mean curvature vector in two-dimensional complex space forms. As a result, we find new examples of such surfaces.
Similar content being viewed by others
References
Chen B.Y. (1973) On the surface with parallel mean curvature vector. Indiana Univ. Math. J. 22: 655–666
Chen B.Y. (1998) Special slant surfaces and a basic inequality, Results Math. 33: 65–78
Dajczer M., Tojeiro R. (1995) Flat totally real submanifolds of CP n and the symmetric generalized wave equation. Tohoku Math. J. 47: 117–123
Eschenburg J.H., Guadalupe I.V., Tribuzy R.A. (1985) The fundamental equations of minimal surfaces in CP 2. Math. Ann. 270: 571–598
Hirakawa S. (2002) On the overdetermined system about surfaces with parallel mean curvature vector field. Kodai Math. J. 25, 246–253
Hirakawa S. (2004) On the periodicity of planes with parallel mean curvature vector in CH 2. Tokyo J. Math. 27: 519–526
Hoffman D. (1973) Surfaces of constant mean curvature in constant curvature manifolds. J. Differential Geom. 8: 161–176
Kenmotsu K., Zhou D. (2000) The classification of the surfaces with parallel mean curvature vector in two-dimensional complex space forms. Amer. J. Math. 122: 295–317
Ogata T. (1995) Surfaces with parallel mean curvature vector in P 2(C). Kodai Math. J. 18: 397–407
Yau S.T. (1974) Submanifolds with constant mean curvature I. Amer. J. Math. 96: 345–366
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hirakawa, S. Constant Gaussian Curvature Surfaces with Parallel Mean Curvature Vector in Two-Dimensional Complex Space Forms. Geom Dedicata 118, 229–244 (2006). https://doi.org/10.1007/s10711-005-9038-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10711-005-9038-8