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Bull. Korean Math. Soc. 2011; 48(6): 1329-1339

Printed November 1, 2011

https://doi.org/10.4134/BKMS.2011.48.6.1329

Copyright © The Korean Mathematical Society.

Obstruction for the existence of a parallel volume form

Hee-Kyung Cho, Daeyong Kim, and Hyuk Kim

Seoul National University, Seoul National University

Abstract

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For a manifold with a linear connection, we find an obstruction class to have a volume form parallel with respect to its connection which corresponds to the Chern-Simons secondary invariant in the frame bundle of the manifold.

Keywords: parallel volume form, parallel volume obstruction class

MSC numbers: 53B05, 53C05

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