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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.
and 23 Related for: History of manifolds and varieties information
The study ofmanifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear...
timeline ofmanifolds, one of the major geometric concepts of mathematics. For further background see historyofmanifoldsandvarieties. Manifolds in contemporary...
less general than manifolds extrinsically defined as submanifolds of Euclidean space. See also the historyofmanifoldsandvarieties for context. Although...
just a point. Complex manifolds that can be embedded in Cn are called Stein manifoldsand form a very special class ofmanifolds including, for example...
(e.g. CT scans). Manifolds can be equipped with additional structure. One important class ofmanifolds are differentiable manifolds; their differentiable...
concerned with the study of spaces such as complex manifoldsand complex algebraic varieties, functions of several complex variables, and holomorphic constructions...
of Riemannian manifolds, Darboux's theorem states that all symplectic manifolds are locally isomorphic. The only invariants of a symplectic manifold are...
general manifolds. Banach manifoldsand Fréchet manifolds, in particular manifoldsof mappings are infinite dimensional differentiable manifolds. For a...
aspect of complex geometry is that there are continuous families of non-isomorphic complex manifolds (which are all diffeomorphic as real manifolds). Phillip...
Whereas Michael Freedman classified topological four-manifolds, Donaldson's work focused on four-manifolds admitting a differentiable structure, using instantons...
differentiable manifolds, the dimension is also the dimension of the tangent vector space at any point. In geometric topology, the theory ofmanifolds is characterized...
relation to the classification of three-folds. Mori completed his Ph.D. titled "The Endomorphism Rings of Some Abelian Varieties" under Masayoshi Nagata at...
International Congress of Mathematicians in Zürich, Kontsevich (1994) speculated that mirror symmetry for a pair of Calabi–Yau manifolds X and Y could be explained...
important to the study of compact complex manifoldsand complex projective varieties ( C P n {\displaystyle \mathbb {CP} ^{n}} ) and has a different flavour...
geometry deals with complex manifoldsand the more general analytic spaces defined locally by the vanishing of analytic functions of several complex variables...
varieties in a way which is very similar to its use in the study of differential and analytic manifolds. This is obtained by extending the notion of point:...
the choices of finite field correspond to the finite primes of the number field. Abelian varieties appear naturally as Jacobian varieties (the connected...
the Calabi–Yau manifolds (and also the hyperkähler manifolds) of dimension two. As such, they are at the center of the classification of algebraic surfaces...
complex geometry and algebraic geometry. The primary objects of study in complex geometry are complex manifolds, complex algebraic varieties, and complex analytic...
before Newton and Leibniz (M.A.). University of Colorado. OCLC 48160073. Wikiquote has quotations related to Historyof calculus. A historyof the calculus...
vector fields on the manifold itself, it should be relevant to study the deformations of projective embeddings of Kähler manifolds under holomorphic vector...
The historyof mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern...
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