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1955 Dimensional differentiation of harmonic tensors for variations of Riemannian metric
Tatsuo Nakae
Mem. College Sci. Univ. Kyoto Ser. A Math. 29(1): 43-53 (1955). DOI: 10.1215/kjm/1250777319

Abstract

The purpose of this paper is to find some properties of harmonic tensors defined in a domain with boundary, when the Riemannian metric undergoes an infinitesimal change. The variations of characteristic roots and Green’s tensor are obtained. The notion of abstract dimension is introduced to preserve the duality between differential and codifferential under the change of metric. An application of the abstract dimension to a physical problem is in the last paragraph.

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Tatsuo Nakae. "Dimensional differentiation of harmonic tensors for variations of Riemannian metric." Mem. College Sci. Univ. Kyoto Ser. A Math. 29 (1) 43 - 53, 1955. https://doi.org/10.1215/kjm/1250777319

Information

Published: 1955
First available in Project Euclid: 20 August 2009

zbMATH: 0065.14704
MathSciNet: MR88761
Digital Object Identifier: 10.1215/kjm/1250777319

Rights: Copyright © 1955 Kyoto University

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