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.

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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.

Optimal transport techniques in the geometric analysis of spaces with curvature bounds

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.

Elliptic PDEs on Compact Ricci Limit Spaces and Applications

and Sawaki, S., Riemannian manifolds admitting a conformal transformation group, J.

Ricci solitons in N(K)-manifold

First, the initial dictionary is achieved by k-means on Riemannian manifolds using the Frechet mean [29].

Ground-Based Cloud-Type Recognition Using Manifold Kernel Sparse Coding and Dictionary Learning

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:

On the new approach for the energy of elastica/Sobre a nova abordagem para a energia da elastica

Carriazo ([6])), and in almost product Riemannian manifolds (B.

Slant and Semi-Slant Submanifolds in Metallic Riemannian Manifolds

The most fundamental examples of geodesic spaces are normed vector spaces, complete Riemannian manifolds, and polyhedral complexes of piecewise constant curvature.

Generalized CAT(0) spaces

Consider ([M.sub.1], [g.sub.1]) and ([M.sub.2], [g.sub.2]) two Riemannian manifolds of dimensions n and m, respectively.

Golden warped product Riemannian manifolds

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]).

Escape rate of the Brownian motions on hyperbolic spaces

The energy of a differentiable map f: (M, g) [right arrow] (N, h) between Riemannian manifolds is given by

A Novel Condition to the Harmonic of the Velocity Vector Field of a Curve in [R.sup.n]

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.

Calabi-Yau Manifolds, Hermitian Yang-Mills Instantons, and Mirror Symmetry

First, images are represented as Riemannian manifolds embedded in a higher dimensional spatial-feature manifold.

Unsupervised Joint Image Denoising and Active Contour Segmentation in Multidimensional Feature Space