Overview

The study of curves and surfaces forms an important part of classical differential geometry. Differential Geometry of Curves and Surfaces: A Concise Guide presents traditional material in this field along with important ideas of Riemannian geometry. The author introduces the reader to curves, then progresses to surfaces and finally to more complex topics in the concluding section. The book weaves together standard theoretical material with more difficult theorems and complex problems while maintaining an easy separation between the two. One of the striking features of this presentation is the large number of non-trivial and original problems, some with useful hints and solutions, which introduce a motivated student into the real world of geometry. Another strong point is the non-trivial material connected with the Aleksandrov global angle comparison theorem. Its generalization for Riemannian spaces of arbitrary dimension is known as the celebrated Toponogov comparison theorem - one of the cornerstones of modern Riemannian geometry. This rigorous exposition, with well-motivated topics, is ideal for advanced undergraduate students, and first year graduate students.

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9780817643843

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Reviews

From the reviews: <p> This book by the late author covers a ] the subjects which are normally taught in a course on the differential geometry of curves and surfaces. a ] It can be recommended for first-year graduate students and also for use in the classroom. a ] the book is rich in geometry and concrete examples. a ] the book is very welcome since it is an original contribution in various aspects and gives a number of geometric insights a ] . Numerous illustrations make the reading enjoyable. (Wolfgang KA1/4hnel, Mathematical Reviews, Issue 2006 m) <p> Toponogova (TM)s a ~concise guidea (TM) to elementary differential geometry has the potential to be a useful reference and/or review book a ] . (Fernando Q. GouvA]a, MathDL, March, 2006)

<p>From the reviews: <p><p> This book by the late author covers the subjects which are normally taught in a course on the differential geometry of curves and surfaces. It can be recommended for first-year graduate students and also for use in the classroom. the book is rich in geometry and concrete examples. the book is very welcome since it is an original contribution in various aspects and gives a number of geometric insights . Numerous illustrations make the reading enjoyable. (Wolfgang K hnel, Mathematical Reviews, Issue 2006 m)<p> Toponogov 's concise guide to elementary differential geometry has the potential to be a useful reference and/or review book . (Fernando Q. Gouv a, MathDL, March, 2006)

From the reviews: This book by the late author covers ... the subjects which are normally taught in a course on the differential geometry of curves and surfaces. ... It can be recommended for first-year graduate students and also for use in the classroom. ... the book is rich in geometry and concrete examples. ... the book is very welcome since it is an original contribution in various aspects and gives a number of geometric insights ... . Numerous illustrations make the reading enjoyable. (Wolfgang Kuhnel, Mathematical Reviews, Issue 2006 m) Toponogov's `concise guide' to elementary differential geometry has the potential to be a useful reference and/or review book ... . (Fernando Q. Gouvea, MathDL, March, 2006) This book, written by one of the Russian masters, offers a comprehensive introduction to classical differential geometry of curves and surfaces. Only a basic background in analysis and linear algebra is needed to follow the presentation. ... A distinctive feature of the book is that, apart from a large number of exercises, it also contains many original problems with outlines of solutions. (A. Cap, Monatshefte fur Mathematik, Vol. 155 (1), September, 2008)

From the reviews: This book by the late author covers ! the subjects which are normally taught in a course on the differential geometry of curves and surfaces. ! It can be recommended for first-year graduate students and also for use in the classroom. ! the book is rich in geometry and concrete examples. ! the book is very welcome since it is an original contribution in various aspects and gives a number of geometric insights ! . Numerous illustrations make the reading enjoyable. (Wolfgang Kuhnel, Mathematical Reviews, Issue 2006 m) Toponogov's 'concise guide' to elementary differential geometry has the potential to be a useful reference and/or review book ! . (Fernando Q. Gouvea, MathDL, March, 2006)

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