Matches in DBpedia 2015-10 for { ?s ?p "The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra and topology. Certain special classes of manifolds also have additional algebraic structure; they may behave like groups, for instance. In that case, they are called Lie Groups. Alternatively, they may be described by polynomial equations, in which case they are called algebraic varieties, and if they additionally carry a group structure, they are called algebraic groups.The term "manifold" comes from German Mannigfaltigkeit, by Riemann.In Romance languages, this is translated as "variety" – such spaces with a differentiable structure are called "analytic varieties", while spaces with an algebraic structure are called "algebraic varieties".In English, "manifold" refers to spaces with a differentiable or topological structure, while "variety" refers to spaces with an algebraic structure, as in algebraic varieties."@en }
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- History_of_manifolds_and_varieties abstract "The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra and topology. Certain special classes of manifolds also have additional algebraic structure; they may behave like groups, for instance. In that case, they are called Lie Groups. Alternatively, they may be described by polynomial equations, in which case they are called algebraic varieties, and if they additionally carry a group structure, they are called algebraic groups.The term "manifold" comes from German Mannigfaltigkeit, by Riemann.In Romance languages, this is translated as "variety" – such spaces with a differentiable structure are called "analytic varieties", while spaces with an algebraic structure are called "algebraic varieties".In English, "manifold" refers to spaces with a differentiable or topological structure, while "variety" refers to spaces with an algebraic structure, as in algebraic varieties.".