Differential Geometry and Its Applications

With its hearty history and its many triumphs in the study of everything from the fundamentals of nature to DNA, differential geometry is not an ordinary branch of mathematics. Oprea (mathematics, Cleveland State U.) argues that differential geometry combines features of geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations and ideas taken from the sciences, and makes his case for taking his point of view with this undergraduate text that works with computer algebra programs to achieve visible results. Along the way he covers the geometry of curves, surfaces, curvatures, constant mean curvature surfaces, geodesics, metrics, isometries, holonomy and the Gauss-Bonnet theorem, the calculations of variations and geometry, and higher dimensions, just for fun. Annotation c2007 Book News, Inc., Portland, OR (booknews.com)

John Oprea was born in Cleveland, Ohio and was educated at Case Western Reserve University and at Ohio State University. He received his PhD at OSU in 1982 and, after a post-doc at Purdue university, he began his tenure at Cleveland State in 1985. Oprea is a member of the Mathematical Association of America and the America Mathematical Society. He is an Associate Editor of the Journal of Geometry and Symmetry in Physics. In 1996, Oprea was awarded the MAA’s Lester R. Ford award for his Monthly article, “Geometry and the Foucault Pendulum.” Besides various journal articles on topology and geometry, he is also the author of The Mathematics of Soap Films (AMS Student Math Library, volume 10), Symplectic Manifolds with no Kahler Structure (with A. Tralle, Springer Lecture Notes in Mathematics, volume 1661), Lusternik-Schnirelmann Category (with O. Cornea, G. Lupton and D. Tanre, AMS Mathematical Surveys and Monographs, volume 103) and the forthcoming Algebraic Models in Geometry (with Y. Felix and D. Tanre, for Oxford University Press).