Riemannian manifold

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Riemannian manifold

[rē′män·ē·ən ′man·ə‚fōld]
(mathematics)
A differentiable manifold where the tangent vectors about each point have an inner product so defined as to allow a generalized study of distance and orthogonality.
References in periodicals archive ?
The approachwill be used also to establish new quantitative versions of classical geometric/functional inequalities for smooth riemannian manifolds and to make progress in long standing open problems for both riemannian and sub-riemannian manifolds.theme iii will investigate optimal transport in a lorentzian setting, where the ricci curvature plays a keyrole in einstein~s equations of general relativity.
This volume examines elliptic PDEs (partial differential equations) on compact Gromov-Hausdorff limit spaces of Riemannian manifolds with lower Ricci curvature bounds, specifically establishing continuities of geometric quantities, which include solutions of Poisson's equations, eigenvalues of Schr|dinger operators, generalized Yamabe constants, and eigenvalues of the Hodge Laplacian, with respect to the Gromov-Hausdorff topology.
and Sawaki, S., Riemannian manifolds admitting a conformal transformation group, J.
First, the initial dictionary is achieved by k-means on Riemannian manifolds using the Frechet mean [29].
Definition 3.1: For two Riemannian manifolds (M, p) and (N, [??]) the energy of a differentiable map f: (M, [rho]) [right arrow] (N, [??]) can be defined as:
Carriazo ([6])), and in almost product Riemannian manifolds (B.
The most fundamental examples of geodesic spaces are normed vector spaces, complete Riemannian manifolds, and polyhedral complexes of piecewise constant curvature.
Consider ([M.sub.1], [g.sub.1]) and ([M.sub.2], [g.sub.2]) two Riemannian manifolds of dimensions n and m, respectively.
For the Brownian motions on Riemannian manifolds, more generally symmetric diffusion processes generated by regular Dirichlet forms, upper and lower rate functions are given in terms of volume growth rate ([1-4,6,11]).
The energy of a differentiable map f: (M, g) [right arrow] (N, h) between Riemannian manifolds is given by
In this paper we will explore the gauge theory formulation of six-dimensional Riemannian manifolds to address the issue why CY manifolds exist with a mirror pair.
First, images are represented as Riemannian manifolds embedded in a higher dimensional spatial-feature manifold.