IJPAM: Volume 41, No. 4 (2007)


Gregory L. Light
Providence College
Providence, Rhode Island, 02918, USA
e-mail: glight@providence.edu

Abstract.This paper introduces Einstein tensor $E$ to a calculation of the energy contents of a general $k-$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 $k-$manifold, we apply $E$ to input-output systems, wherein we give a brief review of the connections from the metric $g$, to the Christoffel symbols, to the Riemann-Christoffel curvature tensor, to the Ricci curvature tensors, and finally to $E$ and the stress-energy tensor $T$. 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
ISSN: 1311-8080
Year: 2007
Volume: 41
Issue: 4