Results 11 to 20 of about 2,836 (190)

THE RIEMANNIAN MANIFOLD OF ALL RIEMANNIAN METRICS

The Quarterly Journal of Mathematics, 1991
The space of all Riemannian metrics on a smooth second countable finite dimensional manifold is itself a smooth manifold modeled on the space of symmetric (0,2)-tensor fields with compact support. It carries a canonical Riemannian metric which is invariant under the action of the diffeomorphism group.
Gil-Medrano, Olga, Michor, Peter W.
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The left-invariant contact metric structure on the Sol manifold

Учёные записки Казанского университета: Серия Физико-математические науки, 2020
Among the known eight-dimensional Thurston geometries, there is a geometry of the Sol manifold – a Lie group consisting of real special matrices. For a left-invariant Riemannian metric on the Sol manifold, the left shift group is a maximal simple ...
V.I. Pan’zhenskii, A.O. Rastrepina
doaj   +1 more source

A remark on the metric dimension in Riemannian manifolds of constant curvature [PDF]

AUT Journal of Mathematics and Computing
We compute the metric dimension of Riemannian manifolds of constant curvature. We define the edge weghited metric dimension of the geodesic graphs in Riemannian manifolds and we show that each complete geodesic graph $G=(V,E)$ embedded in a Riemannian ...
Shiva Heidarkhani Gilani, Reza Mirzaie, Ebrahim Vatandoost   +2 more
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Anisotropically Weighted and Nonholonomically Constrained Evolutions on Manifolds

Entropy, 2016
We present evolution equations for a family of paths that results from anisotropically weighting curve energies in non-linear statistics of manifold valued data. This situation arises when performing inference on data that have non-trivial covariance and
Stefan Sommer
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Geodesics of Random Riemannian Metrics [PDF]

Communications in Mathematical Physics, 2014
55 pages.
LaGatta, Tom, Wehr, Jan
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Design and visualization of Riemannian metrics

CoRR, 2020
Local and global illumination were recently defined in Riemannian manifolds to visualize classical Non-Euclidean spaces. This work focuses on Riemannian metric construction in $\mathbb{R}^3$ to explore special effects like warping, mirages, and deformations.
Tiago Novello, Vinícius da Silva, Luiz Velho 0001   +2 more
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Geometry without topology as a new conception of geometry

International Journal of Mathematics and Mathematical Sciences, 2002
A geometric conception is a method of a geometry construction. The Riemannian geometric conception and a new T-geometric one are considered. T-geometry is built only on the basis of information included in the metric (distance between two points).
Yuri A. Rylov
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Computing Bi-Invariant Pseudo-Metrics on Lie Groups for Consistent Statistics

Entropy, 2015
In computational anatomy, organ’s shapes are often modeled as deformations of a reference shape, i.e., as elements of a Lie group. To analyze the variability of the human anatomy in this framework, we need to perform statistics on Lie groups. A Lie group
Nina Miolane, Xavier Pennec
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On the geometry of $Diff(S^1)$-pseudodifferential operators based on renormalized traces.

Pracì Mìžnarodnogo Geometričnogo Centru, 2021
In this article, we examine the geometry of a group of Fourier-integral operators, which is the central extension of $Diff(S^1)$ with a group of classical pseudo-differential operators of any order.
Jean-Pierre Magnot
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Flag curvatures of the unit sphere in a Minkowski-Randers space [PDF]

AUT Journal of Mathematics and Computing, 2021
On a real vector space $V$, a Randers norm $\hat{F}$ is defined by $\hat{F}=\hat{\alpha}+\hat{\beta}$, where $\hat{\alpha}$ is a Euclidean norm and $\hat{\beta}$ is a covector.
Libing Huang, Haibin Su
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