Results 11 to 20 of about 1,380,597 (301)
Geometry without topology as a new conception of geometry [PDF]
International Journal of Mathematics and Mathematical Sciences, 2001 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).
Rylov, Yuri A.
core +5 more sources
Riemannian geometry of Lie algebroids
Journal of the Egyptian Mathematical Society, 2011 typos corrected references ...
Mohamed Boucetta
openaire +5 more sources
Non-Riemannian geometry of M-theory [PDF]
Journal of High Energy Physics, 2019 We construct a background for M-theory that is moduli free. This background is then shown to be related to a topological phase of the E8(8) exceptional field theory (ExFT).
D. Berman, Chris D. A. Blair, Ray Otsuki
semanticscholar +3 more sources
Introduction to differential and Riemannian geometry [PDF]
Riemannian Geometric Statistics in Medical Image Analysis, 2020 International audience; This chapter introduces the basic concepts of differential geometry: Manifolds, charts, curves, their derivatives, and tangent spaces. The addition of a Riemannian metric enables length and angle measurements on tangent spaces giving rise to the notions of curve length, geodesics, and thereby the basic constructs for statistical
S. Sommer, Tom Fletcher, X. Pennec
semanticscholar +5 more sources
Generalized pseudo-Riemannian geometry [PDF]
Transactions of the American Mathematical Society, 2002 Generalized tensor analysis in the sense of Colombeau’s construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of generalized functions, we define the notions of generalized pseudo-Riemannian metric, generalized connection and ...
Michael Kunzinger, Roland Steinbauer
openalex +5 more sources
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
openalex +6 more sources
Sub-Riemannian geometry and Lie groups. Part II. Curvature of metric spaces, coadjoint orbits and associated representations [PDF]
arXiv, 2004 This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups. Part I", math.MG/0210189, available at http://arxiv.org/abs/math.MG/0210189, and "Tangent bundles to sub-Riemannian groups", math.MG/0307342, available at http://arxiv.org/abs ...
Buliga, Marius
arxiv +3 more sources
A Survey of Riemannian Contact Geometry
Complex Manifolds, 2019 This survey is a presentation of the five lectures on Riemannian contact geometry that the author gave at the conference “RIEMain in Contact”, 18-22 June 2018 in Cagliari, Sardinia.
D. Blair
semanticscholar +2 more sources
Decoding Multi-Class Motor Imagery and Motor Execution Tasks Using Riemannian Geometry Algorithms on Large EEG Datasets. [PDF]
Sensors (Basel), 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
Shuqfa Z, Belkacem AN, Lakas A.
europepmc +2 more sources
Riemannian Holonomy and Algebraic Geometry
, 1999 This survey paper is devoted to Riemannian manifolds with special holonomy. To any Riemannian manifold of dimension n is associated a closed subgroup of SO(n), the holonomy group; this is one of the most basic invariants of the metric.
Beauville, A.
core +4 more sources