Proves Kiyohara's 2001 metrics with arbitrary high-degree polynomial integrals are not superintegrable, solving two Bolsinov-Kozlov-Fomenko conjectures via a new theorem on Poisson brackets of integrals.
Intelligent Networks and Systems Society , year =
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Killing tensors on products of Riemannian manifolds with one compact factor are reducible sums of factor tensors.
GTSA-PCA replaces global PCA covariance with curvature-weighted local operators and a geodesic alignment step to produce geometry-aware embeddings that improve on standard PCA and UMAP in small-sample high-curvature settings.
Constructs a Riemannian metric on the 2-torus such that its universal cover does not admit global Riemann normal coordinates.
citing papers explorer
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Real-analyticity of 2-dimensional superintegrable metrics and solution of two Bolsinov-Kozlov-Fomenko conjectures
Proves Kiyohara's 2001 metrics with arbitrary high-degree polynomial integrals are not superintegrable, solving two Bolsinov-Kozlov-Fomenko conjectures via a new theorem on Poisson brackets of integrals.
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Killing tensors on reducible spaces
Killing tensors on products of Riemannian manifolds with one compact factor are reducible sums of factor tensors.
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Curvature-Aware PCA with Geodesic Tangent Space Aggregation for Semi-Supervised Learning
GTSA-PCA replaces global PCA covariance with curvature-weighted local operators and a geodesic alignment step to produce geometry-aware embeddings that improve on standard PCA and UMAP in small-sample high-curvature settings.
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On the existence of geodesic vector fields on closed surfaces
Constructs a Riemannian metric on the 2-torus such that its universal cover does not admit global Riemann normal coordinates.