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Ricci theorem

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In order that a surface with metric and Gaussian curvature be locally isometric to some minimal surface it is necessary and sufficient that (at all points where ) the metric be of Gaussian curvature .

There are generalizations [1], describing Riemannian metrics which arise as metrics of minimal submanifolds in Euclidean spaces of arbitrary dimension.

References

[1] S.-S. Chern, R. Osserman, "Remarks on the Riemannian metrics of a minimal submanifold" E. Looijenga (ed.) D. Siersma (ed.) F. Takens (ed.) , Geometry Symp. (Utrecht, 1980) , Lect. notes in math. , 894 , Springer (1981) pp. 49–90
How to Cite This Entry:
Ricci theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Ricci_theorem&oldid=48538
This article was adapted from an original article by I.Kh. Sabitov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article