A differentiable variety, commonly referred to as a manifold, is a mathematical structure that resembles Euclidean space locally, allowing for the application of analytical and topological methods. In algebraic geometry, varieties are defined as the zeros of multivariate polynomials, leading to the study of algebraic varieties through ring theory. Differentiable varieties, on the other hand, are explored using differential geometry techniques. The discussion emphasizes the distinction between algebraic and differentiable varieties while suggesting the inclusion of algorithm varieties as a third category relevant to computer science.
PREREQUISITESMathematicians, students of geometry, computer scientists, and anyone interested in the theoretical foundations of algebraic and differentiable varieties.
This isn't the place, neither for a lecture in algebraic geometry, nor in differential geometry. How could I answer such a question? They are surfaces as you have said, defined by equations. So this answers your question and probably simultaneously doesn't. Can you be more specific? Otherwise I have to recommend our Science and Math Textbooks forum, where you can find or ask for appropriate book recommendations.Opressor said:... I still do not know what it is!