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Book review

Author(s) Burago, Yu.D.
Shefel', S.Z.
Rozendorn, E.R.
Sabitov, I.Kh.
Title Geometry III (Theory of Surfaces)
Publisher Springer-Verlag
Year of publication 1992
Reviewed by Daniel Vacaretu

This volume belongs to the series: Encyclopedia of Mathematica1 Sciences, being the English translation of a Russian version published in 1989 by Publisher VINITI, Moscow.

The book contains three parts meant to be read independently, and so together:

I: The Geometry of Surfaces in Euclidean Spaces by Yu.D. Burago and S.R. Shefel'

II: Surfaces of Negative Curvature by E.R. Rozendorn

III: Local Theory of Bendings of Surfaces: by I.Kh. Sabitov

The first part of the book is about the problem of the connection between classes of metrics and classes of surfaces in E^n. The first chapter is a brief survey of general questions in the theory of surfaces from this point of view. Chaptere 2 and 3 are devoted to a more detailed consideration of convex and saddle surfaces respectively. The subject of Chapter 4 consists of classes of metrics not associated directly with the condition that the Gaussian curvature has a definite sign, and G-stable immersions of them.

The second part is devoted to surfaces of negative Gaussian curvature in three-dimensional Euclidean space E^3 and related probless.

In the third part the authors are concerned mainly with local questions of the theory of bendings of two dimensional surfaces in three-dimensional Euclidean space.

Each part of this volume contains a good list of references, each of them very rich, even exhaustive.

The book is designed for research workers as well as for students of different mathematical faculties and it should be a good acquisition for libraries and for individuals.