Diffeomorphisms and volume-preserving embeddings of noncompact manifolds
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- by R. E. Greene and K. Shiohama PDF
- Trans. Amer. Math. Soc. 255 (1979), 403-414 Request permission
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.References
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 255 (1979), 403-414
- MSC: Primary 58D10; Secondary 53C42
- DOI: https://doi.org/10.1090/S0002-9947-1979-0542888-3
- MathSciNet review: 542888