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Rotation-based metric on the Riemannian manifold of SPD matrices with applications to source data selection for brain-computer interface transfer learning [PDF]
Frontiers in Human NeuroscienceThis paper introduces the pole ratio metric and presents a sphere-based view of symmetric positive-definite matrix rotations on the Riemannian manifold of symmetric positive-definite matrices equipped with the affine-invariant Riemannian metric. The pole
Frida Heskebeck +2 more
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The Riemannian L 2 topology on the manifold of Riemannian metrics [PDF]
Annals of Global Analysis and Geometry, 2010 We study the manifold of all Riemannian metrics over a closed, finite-dimensional manifold. In particular, we investigate the topology on the manifold of metrics induced by the distance function of the L^2 Riemannian metric - so called because it induces an L^2 topology on each tangent space.
exaly +4 more sources
Mathematische Zeitschrift, 1984 The purpose of this paper is to construct a smoothing operator which transforms Riemannian metrics with bounded curvature on compact manifolds into Riemannian metrics with essentially the same curvature bounds and, in addition, bounds on the derivatives of the curvature tensor.
Ruh, Ernst A., Min-Oo,, Bemelmans, Josef
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Weighted Ricci curvature in Riemann-Finsler geometry [PDF]
AUT Journal of Mathematics and Computing, 2021 Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold.
Zhongmin Shen
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Semi-Invariant Riemannian Submersions with Semi-Symmetric Non-Metric Connection
Journal of New Theory, 2021 In this paper, we investigate semi-invariant Riemannian submersion from a Kaehler manifold with semi-symmetric non-metric connection to a Riemannian manifold. We study the geometry of foliations with semi-symmetric non-metric connection.
Ramazan Sarı
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On the geometry of the tangent bundle with gradient Sasaki metric [PDF]
Arab Journal of Mathematical Sciences, 2023 Purpose – Let (M, g) be a n-dimensional smooth Riemannian manifold. In the present paper, the authors introduce a new class of natural metrics denoted by gf and called gradient Sasaki metric on the tangent bundle TM. The authors calculate its Levi-Civita
Lakehal Belarbi, Hichem Elhendi
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On Finsler warped product metrics with vanishing $E$-curvature [PDF]
AUT Journal of Mathematics and Computing, 2021 In this paper, we study Finsler warped product metric recently introduced by P. Marcal and Z. Shen and find characteristics differential equations for this metric to have vanishing $E$-curvature.
Ranadip Gangopadhyay +2 more
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Integral Formulas for Almost Product Manifolds and Foliations
Mathematics, 2022 Integral formulas are powerful tools used to obtain global results in geometry and analysis. The integral formulas for almost multi-product manifolds, foliations and multiply twisted products of Riemannian, metric-affine and sub-Riemannian manifolds, to ...
Vladimir Rovenski
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Relay Placement for Maximum Flow Rate via Learning and Optimization Over Riemannian Manifolds
IEEE Transactions on Machine Learning in Communications and Networking, 2023 Networks topology can be represented over Riemannian manifolds (i.e., curved surfaces), given the symmetric positive definite (SPD) property of their spectral graphs.
Imtiaz Nasim, Ahmed S. Ibrahim
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IEEE Access, 2022 Covariance matrices of spatially-correlated wireless channels in millimeter wave (mmWave) vehicular networks can be employed to design environment-aware beamforming codebooks.
Imtiaz Nasim, Ahmed S. Ibrahim
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