Results 61 to 70 of about 1,198,709 (262)

On noncommutative and pseudo-Riemannian geometry [PDF]

Journal of Geometry and Physics, 2006
We introduce the notion of a semi-Riemannian spectral triple which generalizes the notion of spectral triple and allows for a treatment of semi-Riemannian manifolds within a noncommutative setting. It turns out that the relevant spaces in noncommutative semi-Riemannian geometry are not Hilbert spaces any more but Krein spaces, and Dirac operators are ...
openaire   +4 more sources

Riemannian foliations of bounded geometry [PDF]

Mathematische Nachrichten, 2014
Continuing the study of bounded geometry for Riemannian foliations, begun by Sanguiao, we introduce a chart‐free definition of this concept. Our main theorem states that it is equivalent to a condition involving certain normal foliation charts. For this type of charts, it is also shown that the derivatives of the changes of coordinates are uniformly ...
Jesús A. Álvarez López, Eric Leichtnam, Yuri A. Kordyukov   +2 more
openaire   +3 more sources

On semi-slant $\xi^\perp-$Riemannian submersions

, 2017
The aim of the present paper to define and study semi-slant $\xi^\perp-$Riemannian submersions from Sasakian manifolds onto Riemannian manifolds as a generalization of anti-invariant $\xi^\perp-$Riemannian submersions, semi-invariant $\xi^\perp ...
Akyol, Mehmet Akif, Sarı, Ramazan
core   +1 more source

Transversal Lightlike Submanifolds of Metallic Semi-Riemannian Manifolds

, 2018
The Metallic Ratio is fascinating topic that continually generated news ideas. A Riemannian manifold endowed with a Metallic structure will be called a Metallic Riemannian manifold.
Erdoğan, Feyza Esra
core   +1 more source

Multispectral Chiral Quasi‐Bound States in the Continuum Enabled Microfluidics for High‐Throughput Molecular Screening and Quantification

Advanced Science, EarlyView.
A microfluidics‐integrated chiral quasi‐BIC metachip is developed that generates strong broadband CD from 0.5–2.0 THz in aqueous environments. A UMAP algorithm processes the resulting multidimensional CD features for simultaneous biomolecular conformation identification and concentration quantification (0.05–0.3 mg dL−1).
Xinyue Liang, Zihan Zhao, Xiaocong Tang, Haiyue Yang, Lanju Liang, Meng Zhao, Cong Wang, Lei Wang, Xumin Ding   +8 more
wiley   +1 more source

Geodesic Vector Fields on a Riemannian Manifold

Mathematics, 2020
A unit geodesic vector field on a Riemannian manifold is a vector field whose integral curves are geodesics, or in other worlds have zero acceleration. A geodesic vector field on a Riemannian manifold is a smooth vector field with acceleration of each of
Sharief Deshmukh, Patrik Peska, Nasser Bin Turki   +2 more
doaj   +1 more source

The rolling problem: overview and challenges

, 2012
In the present paper we give a historical account -ranging from classical to modern results- of the problem of rolling two Riemannian manifolds one on the other, with the restrictions that they cannot instantaneously slip or spin one with respect to the ...
A Agrachev, A Agrachev, A Agrachev, A Chelouah, A Marigo, A Marigo, AM Bloch, AV Borisov, Cartan, Cartan, DJ Montana, DW Stroock, E Grong, EP Hsu, F Alouges, G Bor, H Sussmann, I Zelenko, I Zelenko, IM Singer, J Zimmerman, J-M Bismut, K Hüper, K Hüper, K Nomizu, M Godoy Molina, M Godoy Molina, P Rouchon, PB Gilkey, PE Jupp, R Bryant, R Montgomery, R Murray, RW Sharpe, S Kobayashi, SA Chaplygin, SA Chaplygin, T Sakai, V Jurdjevic, V Jurdjevic, V Jurdjevic, Y Chitour, Y Chitour, Y Chitour, Z Li   +44 more
core   +2 more sources

Optimal control in nonequilibrium systems: Dynamic Riemannian geometry of the Ising model. [PDF]

Physical review. E, Statistical, nonlinear, and soft matter physics, 2015
A general understanding of optimal control in nonequilibrium systems would illuminate the operational principles of biological and artificial nanoscale machines.
Grant M. Rotskoff, G. Crooks
semanticscholar   +1 more source

Riemannian Geometry for the Classification of Brain States with Intracortical Brain Recordings

Advanced Intelligent Systems, EarlyView.
Geometric machine learning is applied to decode brain states from invasive intracortical neural recordings, extending Riemannian methods to the invasive regime where data is scarcer and less stationary. A Minimum Distance to Mean classifier on covariance manifolds uses geodesic distances to outperform convolutional neural networks while reducing ...
Arnau Marin‐Llobet, Sergio Sánchez‐Manso, Arnau Manasanch, Lluc Tresserras, Xinhe Zhang, Yining Hua, Hao Zhao, Melody Torao‐Angosto, Maria V Sanchez‐Vives, Leonardo Dalla Porta   +9 more
wiley   +1 more source

The χ-Hessian Quotient for Riemannian Metrics

Axioms, 2021
Pseudo-Riemannian geometry and Hilbert–Schmidt norms are two important fields of research in applied mathematics. One of the main goals of this paper will be to find a link between these two research fields. In this respect, in the present paper, we will
Pişcoran Laurian-Ioan, Akram Ali, Barbu Cătălin, Ali H. Alkhaldi   +3 more
doaj   +1 more source