IJPAM: Volume 41, No. 4 (2007)
Providence, Rhode Island, 02918, USA
Abstract.This paper introduces Einstein tensor to a calculation of the energy contents of a general dimensional manifold by evaluating all the local curvatures. Since in management science the construct of input-output systems is fundamental and is amenable to a modeling by a manifold, we apply to input-output systems, wherein we give a brief review of the connections from the metric , to the Christoffel symbols, to the Riemann-Christoffel curvature tensor, to the Ricci curvature tensors, and finally to and the stress-energy tensor . As an illustration, we compute the Ricci curvature tensors for a Monge patch and apply them to a familiar production transformation function, with remarks on the relationships between curvatures and energies.
Received: September 13, 2007
AMS Subject Classification: 53C21, 53A45, 58D17, 93B29
Key Words and Phrases: manifold energy, system stress, curvatures, input-output
Source: International Journal of Pure and Applied Mathematics