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The book "Differential Geometry and Its Applications" by John Oprea is a comprehensive textbook that covers the fundamental concepts of differential geometry. The book is designed for undergraduate and graduate students, as well as researchers, who want to learn about the subject. It provides a clear and concise introduction to the basics of differential geometry, including:
: First and second fundamental forms, shape operators, and various curvatures.
You can find the book through various academic publishers and retailers: Differential Geometry and Its Applications - AMS Bookstore
: The text encourages using computer algebra systems like Maple to visualize abstract concepts.
John Oprea's writing style is known for being clear, concise, and engaging. The book is praised for its:
If you're looking for a PDF version of the book, here are a few suggestions:
Most people ignore appendices. Oprea’s Appendix A ("Linear Algebra Review") and Appendix B ("Calculus Review") are unique. If you are rusty on the cross product, the Jacobian, or eigenvalues, start here. It ensures you don't get lost in Chapter 1.