Results 1 to 10 of about 1,358,030 (306)
Geometry without topology as a new conception of geometry [PDF]
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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Decoding Multi-Class Motor Imagery and Motor Execution Tasks Using Riemannian Geometry Algorithms on Large EEG Datasets [PDF]
Sensors, 2023 The use of Riemannian geometry decoding algorithms in classifying electroencephalography-based motor-imagery brain–computer interfaces (BCIs) trials is relatively new and promises to outperform the current state-of-the-art methods by overcoming the noise
Zaid Shuqfa +2 more
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Discrete Riemannian Geometry [PDF]
Journal of Mathematical Physics, 1998 Within a framework of noncommutative geometry, we develop an analogue of (pseudo) Riemannian geometry on finite and discrete sets. On a finite set, there is a counterpart of the continuum metric tensor with a simple geometric interpretation.
Dimakis, A., Muller-Hoissen, F.
core +5 more sources
The geometry of Riemannian spaces [PDF]
Transactions of the American Mathematical Society, 1934 The primary purpose of this paper is to expose, in as simple and clear a form as is possible, the fundamentals of the geometric structure of a Riemannian space. It is a general truth that the methods which pierce most deeply into the heart of a geometric theory are invariant methods, that is, methods which are independent of the choice of the ...
W. C. Graustein
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Introduction to differential and Riemannian geometry [PDF]
Riemannian Geometric Statistics in Medical Image Analysis, 2020 International ...
S. Sommer, Tom Fletcher, X. Pennec
semanticscholar +6 more sources
The R.I. Pimenov unified gravitation and electromagnetism field theory as semi-Riemannian geometry [PDF]
Phys.Atom.Nucl.72:794-800,2009, 2008 More then forty years ago R.I. Pimenov introduced a new geometry -- semi-Riemannian one -- as a set of geometrical objects consistent with a fibering $ pr: M_n \to M_m.$ He suggested the heuristic principle according to which the physically different quantities (meter, second, coulomb etc.) are geometrically modelled as space coordinates that are not ...
A. Chodos +11 more
arxiv +3 more sources
Motor Imagery EEG Classification Based on Decision Tree Framework and Riemannian Geometry. [PDF]
Comput Intell Neurosci, 2019 This paper proposes a novel classification framework and a novel data reduction method to distinguish multiclass motor imagery (MI) electroencephalography (EEG) for brain computer interface (BCI) based on the manifold of covariance matrices in a ...
Guan S, Zhao K, Yang S.
europepmc +2 more sources
Riemannian geometry of Lie algebroids
Journal of the Egyptian Mathematical Society, 2011 We introduce Riemannian Lie algebroids as a generalization of Riemannian manifolds and we show that most of the classical tools and results known in Riemannian geometry can be stated in this setting.
Mohamed Boucetta
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Riemannian geometry of Hartogs domains [PDF]
International Journal of Mathematics, 2008 Let $D_F = \{(z_0, z) \in {\C}^{n} | |z_0|^2 < b, \|z\|^2 < F(|z_0|^2) \}$ be a strongly pseudoconvex Hartogs domain endowed with the \K metric $g_F$ associated to the \K form $\omega_F = -\frac{i}{2} \partial \bar{\partial} \log (F(|z_0|^2) - \|z\|^2)$.
ANDREA LOI +3 more
core +8 more sources
Poisson-Riemannian geometry [PDF]
Journal of Geometry and Physics, 2017 We study noncommutative bundles and Riemannian geometry at the semiclassical level of first order in a deformation parameter λ, using a functorial approach. This leads us to field equations of ‘Poisson–Riemannian geometry’ between the classical metric, the Poisson bracket and a certain Poisson-compatible connection needed as initial data for the ...
E. Beggs, S. Majid
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