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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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$G$-deformations and some generalizations of H. Weyl’s tube theorem
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by Oldřich Kowalski and Lieven Vanhecke PDF
Trans. Amer. Math. Soc. 294 (1986), 799-811 Request permission

Abstract:

We prove an invariance theorem for the volumes of tubes about submanifolds in arbitrary analytic Riemannian manifolds under $G$-deformations of the second order. For locally symmetric spaces or two-point homogeneous spaces we give stronger invariance theorems using only $G$-deformations of the first order. All these results can be viewed as generalizations of the result of H. Weyl about isometric deformations and the volumes of tubes in spaces of constant curvature. They are derived from a new formula for the volume of a tube about a submanifold.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 294 (1986), 799-811
  • MSC: Primary 53C20
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0825738-0
  • MathSciNet review: 825738