Results 11 to 20 of about 1,198,709 (262)
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.
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Riemannian Geometry of Noncommutative Surfaces [PDF]
Journal of Mathematical Physics, 2008 A Riemannian geometry of noncommutative n-dimensional surfaces is developed as a first step towards the construction of a consistent noncommutative gravitational theory.
A. Tureanu +7 more
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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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A bridge between complex geometry and Riemannian geometry [PDF]
Proceedings of the American Mathematical Society, 1993 Every complex manifold M n {M^n} with holomorphic metric can be obtained (at least locally) from a complex manifold E 2 ∙ n − 2 {E^{2 \bullet n - 2}} and one of its C
Antonio Cassa
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Riemannian Geometry on Quantum Spaces [PDF]
International Journal of Modern Physics A, 1997 An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space.
Pei-Ming Ho
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Riemannian geometry and automatic differentiation for optimization problems of quantum physics and quantum technologies [PDF]
New Journal of Physics, 2020 Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks.
I. Luchnikov, M. Krechetov, S. Filippov
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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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Riemannian Geometry-Based Decoding of the Directional Focus of Auditory Attention Using EEG [PDF]
IEEE International Conference on Acoustics, Speech, and Signal Processing, 2020 Auditory attention decoding (AAD) algorithms decode the auditory attention from electroencephalography (EEG) signals that capture the listener’s neural activity.
Simon Geirnaert +2 more
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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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