Results 321 to 330 of about 6,347,597 (373)

Homogeneous Spaces with Sections

manuscripta mathematica, 2005
Let \(M\) be a connected complete Riemannian manifold. A section in \(M\) is a connected, totally geodesic, homogeneous submanifold \(\Sigma\) with the property that for all geodesics \(\gamma : {\mathbb R} \to M\) there exists an isometry \(g\) of \(M\) such that \(g \cdot \gamma({\mathbb R}) \subset \Sigma\) and \(g \cdot \gamma(0) = p\) for a fixed ...
Kollross, A.   +3 more
openaire   +5 more sources

Invariant surfaces in the homogeneous space Sol with constant curvature

, 2009
A surface in homogeneous space Sol is said to be an invariant surface if it is invariant under some of the two 1‐parameter groups of isometries of the ambient space whose fix point sets are totally geodesic surfaces.
Rafael L'opez, M. Munteanu
semanticscholar   +1 more source

Feature Space Augmentation for Long-Tailed Data

European Conference on Computer Vision, 2020
Real-world data often follow a long-tailed distribution as the frequency of each class is typically different. For example, a dataset can have a large number of under-represented classes and a few classes with more than sufficient data.
Peng Chu   +3 more
semanticscholar   +1 more source

Metrically homogeneous spaces [PDF]

open access: possibleRussian Mathematical Surveys, 2002
Summary: This survey discusses the problem of describing properties of the class of metric spaces in which the Uryson construction of a universal homogeneous metric space (for this class) can be carried out axiomatically. One of the main properties of this kind is the possibility of gluing together two metrics given on closed subsets and coinciding on ...
openaire   +2 more sources

Wavefunctions on Homogeneous Spaces

Journal of Mathematical Physics, 1969
The properties of a class of homogeneous spaces of the Poincaré group are discussed. An 8-dimensional space appears especially promising and the explicit unitary irreducible representations corresponding to physical particles are given using scalar wavefunctions on this space.
Henri Bacry, Arne Kihlberg
openaire   +2 more sources

Generating optical vortex beams by momentum-space polarization vortices centred at bound states in the continuum

, 2019
Optical vortices, beams with spiral wavefronts and screw phase dislocations, have been attracting increasing interest in various fields. Here, we theoretically propose and experimentally realize an easy approach to generating optical vortices.
Bo Wang   +9 more
semanticscholar   +1 more source

ON THE SEMICHARACTERISTICS OF HOMOGENEOUS SPACES

The Quarterly Journal of Mathematics, 1985
This paper analyzes the Kervaire semicharacteristic of homogeneous spaces G/H, \(k(G/H)=\dim H^{2*}(G/H; {\mathbb{Z}}_ 2) (mod 2)\). Particular attention is paid to the case \(G=SU(n)\), and for example, one result is the following Theorem: Let H be a connected simple Lie subgroup of SU(n) with dim(SU(n)/H) odd.
openaire   +2 more sources

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