Hamiltonian Expression of Curvature Tensors in the York Canonical Basis: I) The Riemann Tensor and Ricci Scalars [PDF]
International Journal of Geometric Methods in Modern Physics, 2014 By using the York canonical basis of ADM tetrad gravity, in a formulation using radar 4-coordinates for the parametrization of the 3+1 splitting of the space-time, it is possible to write the 4-Riemann tensor of a globally hyperbolic, asymptotically Minkowskian space-time as a Hamiltonian tensor, whose components are 4-scalars with respect to the ...
L. Lusanna, Massimo Villani
openalex +5 more sources
M-eigenvalues of Riemann Curvature Tensor of Conformally Flat Manifolds [PDF]
, 2018 We generalized Xiang, Qi and Wei's results on the M-eigenvalues of Riemann curvature tensor to higher dimensional conformal flat manifolds. The expression of M-eigenvalues and M-eigenvectors are found in our paper. As a special case, M-eigenvalues of conformal flat Einstein manifold have also been discussed, and the conformal the invariance of M ...
Yun Miao, Liqun Qi, Yimin Wei
openalex +3 more sources
Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature [PDF]
, 2004 Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.
Lee C. Loveridge
openalex +3 more sources
Statistical manifolds with the same statistic and Riemann curvature tensor fields
Boletim da Sociedade Paranaense de MatemáticaThis paper provides a necessary and sufficient condition for an almost contact metric statistical manifold to have the same statistic and Riemann curvature tensor fields, and a condition to determine the uniqueness of such a statistical structures ...
Fereshteh Malek
semanticscholar +3 more sources
A remark on the symmetries of the Riemann curvature tensor [PDF]
, 2002 1 ...
Pavol Ševera
openalex +3 more sources
Properties of concircular curvature tensors on Riemann spaces
Filomat, 2016 This paper studies conditions of pseudo-symmetric and semi-symmetric type on geodesic and subgeodesic related Riemann spaces. Properties of concircular transformations of metrics are characterized, using certain concircular-Riemann type flows. Also concircular-Riemann solitons are introduced, as natural extensions of Ricci solitons.
Iulia-Elena Hirica
openalex +3 more sources
Brownian motion meets Riemann curvature [PDF]
, 2010 The general covariance of the diffusion equation is exploited in order to explore the curvature effects appearing on brownian motion over a d-dimensional curved manifold.
Almeida P F F +11 more
core +2 more sources
2D Riemann-Christoffel curvature tensor via a 3D space using a specialized permutation scheme [PDF]
, 2009 7 pages, 1 ...
Mensur Omerbashich
openalex +3 more sources
The Riemann curvature tensor, its invariants, and their use in the classification of spacetimes
, 2015 The equivalence problem in general relativity is to determine whether two solutions of the Einstein field equations are isometric. Petrov has given a classification of metrics according to their isometry algebras. This talk discusses the use of the Petrov classification scheme, together with the use of scalar curvature invariants, to address the ...
Jesse Hicks
openalex +3 more sources
Curvature Identities for Generalized Kenmotsu Manifolds [PDF]
E3S Web of Conferences, 2021 In the present paper we obtained 2 identities, which are satisfied by Riemann curvature tensor of generalized Kenmotsu manifolds. There was obtained an analytic expression for third structure tensor or tensor of f-holomorphic sectional curvature of GK ...
Ahmad Abu-Saleem +2 more
doaj +1 more source