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International Journal of Mathematics and Mathematical Sciences
Volume 11, Issue 4, Pages 675-682
http://dx.doi.org/10.1155/S0161171288000821

An application of stress energy tensor to the vanishing theorem of differential forms

Department of Mathematics and Statistics, Southern Illinois University at Edwardsville, Edwardsville 62026-1653, Illinois, USA

Received 29 September 1987

Copyright © 1988 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The author applies the stress energy of differential forms to study the vanishing theorems of the Liouville type. It is shown that for a large class of underlying manifolds such as the Euclidean n-space, the complex n-space, and the complex hyperbolic space form, if any vector bundle valued p-form with conservative stress energy tensor is of finite norm or slowly divergent norm, then the p-form vanishes. This generalizes the recent results due to Hu and Sealey.