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Volume of a small Extrinsic Ball in a Submanifold

Volume of a small Extrinsic Ball in a Submanifold For a submanifold Mp ↪ R, we determine a two‐term asymptotic formula for vol (Mp ∩ B∈(x)) for x∈ Mp as ∈ ↓ 0. The second term is a quadratic curvature invariant of the second fundamental form of the imbedding. Imbedded spheres are characterized among compact hypersurfaces by this term. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Volume of a small Extrinsic Ball in a Submanifold

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Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/21.1.87
Publisher site
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Abstract

For a submanifold Mp ↪ R, we determine a two‐term asymptotic formula for vol (Mp ∩ B∈(x)) for x∈ Mp as ∈ ↓ 0. The second term is a quadratic curvature invariant of the second fundamental form of the imbedding. Imbedded spheres are characterized among compact hypersurfaces by this term.

Journal

Bulletin of the London Mathematical Society – Wiley

Published: Jan 1, 1989

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