Results 41 to 50 of about 62,341 (171)

Compatible Metrics of Constant Riemannian Curvature: Local Geometry, Nonlinear Equations, and Integrability

Functional Analysis and Its Applications, 2002
12 ...
openaire   +3 more sources

On Non‐Compact Extended Bach Solitons

Mathematische Nachrichten, EarlyView.
ABSTRACT We study the characterization of non‐compact solitons of the extended Bach flow, known as an extended Bach soliton. We prove that a weakly conformally flat extended Bach soliton (Mn,g,V)$(M^n,g,V)$ with harmonic Weyl tensor is Bach‐flat and the potential vector field V$V$ is conformal.
Rahul Poddar
wiley   +1 more source

Conformal deformations of the Ebin metric and a generalized Calabi metric on the space of Riemannian metrics [PDF]

We consider geometries on the space of Riemannian metrics conformally equivalent to the widely studied Ebin L^2 metric. Among these we characterize a distinguished metric that can be regarded as a generalization of Calabi's metric on the space of K ...
Bauer, Besse, Bourguignon, Brian Clarke, Calabi, Carlen, Clarke, Clarke, DeWitt, Ebin, Fischer, Fischer, Freed, Gil-Medrano, Hamilton, Michor, Michor, Michor, Pekonen, Shah, Tromba, Yanir A. Rubinstein, Yau   +22 more
core   +1 more source

A Geometric Interpretation for the Algebraic Properties of Second‐Order Ordinary Differential Equations

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6912-6917, April 2025.
ABSTRACT Nowadays, a substantial portion of investigations concerning the symmetry analysis of differential equations predominantly adhere to a framework comprising the following key procedures: (i) the derivation of symmetries, (ii) the determination of an optimal system, (iii) the utilization of these symmetries to construct invariants or ...
A. Paliathanasis, S. Moyo, P. G. L. Leach   +2 more
wiley   +1 more source

A Riemannian Dichotomizer Approach on Symmetric Positive Definite Manifolds for Offline, Writer-Independent Signature Verification

Applied Sciences
Automated handwritten signature verification continues to pose significant challenges. A common approach for developing writer-independent signature verifiers involves the use of a dichotomizer, a function that generates a dissimilarity vector with the ...
Nikolaos Vasilakis, Christos Chorianopoulos, Elias N. Zois   +2 more
doaj   +1 more source

The local symmetries of M-theory and their formulation in generalised geometry

, 2011
In the doubled field theory approach to string theory, the T-duality group is promoted to a manifest symmetry at the expense of replacing ordinary Riemannian geometry with generalised geometry on a doubled space.
A Coimbra, A Kleinschmidt, B Julia, B Wit de, C Albertsson, C Albertsson, C Hillmann, C Hull, C Hull, C Hull, D Andriot, David S. Berman, DC Thompson, DS Berman, DS Berman, DS Berman, E Cremmer, G Aldazabal, H Nicolai, Hadi Godazgar, I Jeon, I Jeon, I Jeon, I Jeon, J Thierry-Mieg, JW Barrett, M Graña, Mahdi Godazgar, Malcolm J. Perry, N Hitchin, N Obers, O Hohm, O Hohm, O Hohm, O Hohm, O Hohm, O Hohm, O Hohm, P West, P West, PC West, PC West, PC West, PC West, PP Pacheco, T Courant, T Kugo, W Siegel, W Siegel   +48 more
core   +1 more source

Ellipsoid‐Based Interval‐Type Uncertainty Model Updating Based on Riemannian Manifold and Gaussian Process Model

International Journal of Mechanical System Dynamics, EarlyView.
ABSTRACT Modern engineering systems require advanced uncertainty‐aware model updating methods that address parameter correlations beyond conventional interval analysis. This paper proposes a novel framework integrating Riemannian manifold theory with Gaussian Process Regression (GPR) for systems governed by Symmetric Positive‐Definite (SPD) matrix ...
Yanhe Tao, Qintao Guo, Jin Zhou, Cheng Yi   +3 more
wiley   +1 more source

A strictly local solution to the problem of energy in general relativity

Frontiers in Astronomy and Space Sciences
The problem of energy and its conservation is more than a century old in general relativity (GR) and is considered by many scholars to be, at least, not sufficiently solved.
Werner M. Vieira, Nadja S. Magalhaes
doaj   +1 more source

Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram

, 2008
The local geometry of a Riemannian symmetric space is described completely by the Riemannian metric and the Riemannian curvature tensor of the space. In the present article I describe how to compute these tensors for any Riemannian symmetric space from ...
B.-Y. Chen, C. Chevalley, D.S.P. Leung, O. Loos, S. Helgason, S. Klein, Sebastian Klein   +6 more
core   +2 more sources

Initial State Privacy of Nonlinear Systems on Riemannian Manifolds

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT In this paper, we investigate initial state privacy protection for discrete‐time nonlinear closed systems. By capturing Riemannian geometric structures inherent in such privacy challenges, we refine the concept of differential privacy through the introduction of an initial state adjacency set based on Riemannian distances.
Le Liu, Yu Kawano, Antai Xie, Ming Cao
wiley   +1 more source