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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Diffeomorphisms and volume-preserving embeddings of noncompact manifolds

Authors: R. E. Greene and K. Shiohama
Journal: Trans. Amer. Math. Soc. 255 (1979), 403-414
MSC: Primary 58D10; Secondary 53C42
MathSciNet review: 542888
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Abstract: The theorem of J. Moser that any two volume elements of equal total volume on a compact manifold are diffeomorphism-equivalent is extended to noncompact manifolds: A necessary and sufficient condition (equal total and same end behavior) is given for diffeomorphism equivalence of two volume forms on a noncompact manifold. Results on the existence of embeddings and immersions with the property of inducing a given volume form are also given. Generalizations to nonorientable manifolds and manifolds with boundary are discussed.

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Keywords: Volume form, diffeomorphism, ends of a manifold, volume-preserving embedding, isometric embedding, odd forms
Article copyright: © Copyright 1979 American Mathematical Society