Zobrazeno 1 - 10
of 90
pro vyhledávání: '"McLenaghan, Raymond G"'
The geometric theory of additive separation of variables is applied to the search for multiplicative separated solutions of the bi-Helmholtz equation. It is shown that the equation does not admit regular separation in any coordinate system in any pse
Externí odkaz:
http://arxiv.org/abs/2108.08951
Autor:
Valero, Carlos, McLenaghan, Raymond G.
We review the theory of orthogonal separation of variables on pseudo-Riemannian manifolds of constant non-zero curvature via concircular tensors and warped products. We then apply this theory simultaneously to both the three-dimensional Hyperbolic an
Externí odkaz:
http://arxiv.org/abs/1811.04536
Autor:
Valero, Carlos, McLenaghan, Raymond G.
Publikováno v:
SIGMA 18 (2022), 019, 28 pages
We review a new theory of orthogonal separation of variables on pseudo-Riemannian spaces of constant zero curvature via concircular tensors and warped products. We then apply this theory to three-dimensional Minkowski space, obtaining an invariant cl
Externí odkaz:
http://arxiv.org/abs/1805.12228
Publikováno v:
General Relativity and Gravitation, Vol. 52, No. 2, 03.02.2020
We discuss the design for a discrete, immediate, simple relativistic positioning system (rPS) which is potentially able of self-positioning (up to isometries) and operating without calibration or ground control assistance. The design is discussed in
Externí odkaz:
http://arxiv.org/abs/1805.04741
Publikováno v:
SIGMA 12 (2016), 117, 30 pages
We review the theory of orthogonal separation of variables of the Hamilton-Jacobi equation on spaces of constant curvature, highlighting key contributions to the theory by Benenti. This theory revolves around a special type of conformal Killing tenso
Externí odkaz:
http://arxiv.org/abs/1607.00712
The second order symmetry operators that commute with the Dirac operator with external vector, scalar and pseudo-scalar potentials are computed on a general two-dimensional spin-manifold. It is shown that the operator is defined in terms of Killing v
Externí odkaz:
http://arxiv.org/abs/1407.4855
Publikováno v:
J. Math. Phys. 55.1 (2014)
We study Killing tensors in the context of warped products and apply the results to the problem of orthogonal separation of the Hamilton-Jacobi equation. This work is motivated primarily by the case of spaces of constant curvature where warped produc
Externí odkaz:
http://arxiv.org/abs/1404.3161
We study concircular tensors in spaces of constant curvature and then apply the results obtained to the problem of the orthogonal separation of the Hamilton-Jacobi equation on these spaces. Any coordinates which separate the geodesic Hamilton-Jacobi
Externí odkaz:
http://arxiv.org/abs/1404.2847
We find all orthogonal metrics where the geodesic Hamilton-Jacobi equation separates and the Riemann curvature tensor satisfies a certain equation (called the diagonal curvature condition). All orthogonal metrics of constant curvature satisfy the dia
Externí odkaz:
http://arxiv.org/abs/1404.2565
Publikováno v:
SIGMA 7 (2011), 057
A signature independent formalism is created and utilized to determine the general second-order symmetry operators for Dirac's equation on two-dimensional Lorentzian spin manifolds. The formalism is used to characterize the orthonormal frames and met
Externí odkaz:
http://arxiv.org/abs/1102.0065