On certain infinitesimal isometries of surfaces. (English) Zbl 0671.53005

Isometric deformations of surfaces preserving principal curvatures were first studied by O. Bonnet. Recently, S. S. Chern [Differential geometry and complex analysis, Vol. dedic. H. E. Rauch, 155-163 (1985; Zbl 0566.53002)] has studied such deformations for surfaces of non- constant mean curvature and showed that they turn out to be W-surfaces. In this paper the author characterizes the surfaces of the Euclidean 3- space which admit non-trivial infinitesimal isometries preserving the mean curvature.
Reviewer: T.Hasanis


53A05 Surfaces in Euclidean and related spaces


Zbl 0566.53002
Full Text: EuDML


[1] S. S. Chern: Deformation of Surfaces Preserving Principal Curvatures. Differential Geometry and Complex Analysis, pp. 156-163; Springer-Verlag, Berlin-Heidelberg, 1985. · Zbl 0566.53002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.