172 citations · 305 across the 36 of their papers we have counts for
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Distributions of Distances and Volumes of Balls in Homogeneous Lens Spaces
Brenden Balch, Chris Peterson, Clayton Shonkwiler
Lens spaces are a family of manifolds that have been a source of many interesting phenomena in topology and differential geometry. Their concrete construction, as quotients of odd-…
Expected Distances on Manifolds of Partially Oriented Flags
Brenden Balch, Chris Peterson, Clayton Shonkwiler
Flag manifolds are generalizations of projective spaces and other Grassmannians: they parametrize flags, which are nested sequences of subspaces in a given vector space. These are…
Integral Invariants from Covariance Analysis of Embedded Riemannian Manifolds
Javier Álvarez-Vizoso, Michael Kirby, Chris Peterson
Principal Component Analysis can be performed over small domains of an embedded Riemannian manifold in order to relate the covariance analysis of the underlying point set with the…
Manifold Curvature Descriptors from Hypersurface Integral Invariants
Javier Álvarez-Vizoso, Michael Kirby, Chris Peterson
Integral invariants obtained from Principal Component Analysis on a small kernel domain of a submanifold encode important geometric information classically defined in differential-…
Geometry of Curves in , Singular Value Decomposition, and Hankel Determinants
Xavier Álvarez-Vizoso, Robert Arn, Bruce Draper +2
Let be a parametric curve of class , regular of order . The Frenet-Serret apparatus of at consists of a frame $e_1(t), \dots ,…