Riemannian geometry
Riemannin geometria · elliptinen geometria
Riemannian oor Fins
Riemannian
en
(mathematics) Relating to the branch of geometry inspired by Bernhard Riemann.
Vertalings in die woordeboek Engels - Fins
Riemannin
Geskatte vertalings
Vertoon algoritmies gegenereerde vertalings
Soortgelyke frases
voorbeelde
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Riemannian geometry was first put forward in generality by Bernhard Riemann in the 19th century.
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The second generalization uses differential forms (k-covector fields) instead of vector fields or k-vector fields, and is widely used in mathematics, particularly in differential geometry, geometric topology, and harmonic analysis, in particular yielding Hodge theory on oriented pseudo-Riemannian manifolds.
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Until late 2002, Perelman was best known for his work in comparison theorems in Riemannian geometry.
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More generally, vector calculus can be defined on any 3-dimensional oriented Riemannian manifold, or more generally pseudo-Riemannian manifold.
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This thesis focuses on the role of Riemannian metrics in conformal geometry and on the theory of quasiconformal mappings.
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This also shows that the Riemannian volume form for surfaces is exactly the surface element from vector calculus.
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In the first part he posed the problem of how to define an n-dimensional space and ended up giving a definition of what today we call a Riemannian space.
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The second generalization uses differential forms (k-covector fields) instead of vector fields or k-vector fields, and is widely used in mathematics, particularly in differential geometry, geometric topology, and harmonic analysis, in particular yielding Hodge theory on oriented pseudo-Riemannian manifolds.
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It is shown that if the action of a volume form preserving diffeomorphism has a bounded orbit in the space of Riemannian metrics, then a new Riemannian metric can be found such that the diffeomorphism can be regarded as an isometry.
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The resulting algorithm is known as Riemannian conjugate gradient.
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It is shown that any countable quasiconformal group on a Riemannian manifold (in the introduced sense) can be regarded as a group of conformal mappings with respect to another, optimal, Riemannian metric.
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In a converse manner, another result of this thesis shows that any smooth manifold of dimension 3 or higher admits infinitely many Riemannian metrics such that there is no conformal diffeomorphisms on the manifold.
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Finally, implications of the regularity of Riemannian metrics in conformal geometry are studied.
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Until the autumn of 2002, Perelman was best known for his work in comparison theorems in Riemannian geometry.
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The fundamental quantities in these branches of mathematics are Riemannian metrics that many times define, or emerge as solutions to, nonlinear partial differential equations.
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This thesis presents an efficient Riemannian conjugate gradient algorithm for learning probabilistic models where variational approximation is used.
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One particularly powerful and relatively simple algorithm can be derived by extending conjugate gradient to Riemannian manifolds.
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In general the results of this thesis imply that there is no simple classification of conformal mappings on Riemannian manifolds.
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He published Riemannian Geometry in 1926 and Non-Riemannian Geometry in 1927.
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