Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On an integral formula of Gauss-Bonnet-Grotemeyer


Author: Bang-yen Chen
Journal: Proc. Amer. Math. Soc. 28 (1971), 208-212
MSC: Primary 53.72
MathSciNet review: 0273541
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ e(p)$ and $ G(p)$ be the unit outer normal and the Gauss-Kronecker curvature of an oriented closed even-dimensional hypersurface $ M$ of dimension $ n$ in $ {E^{n + 1}}$. Then for a fixed unit vector $ c$ in $ {E^{n + 1}}$, we have

$\displaystyle (1)\qquad \begin{array}{*{20}{c}} {\int_M^{} {{{({\text{c}}\cdot{... ...2,4, \cdots ,} \\ { = 0,} & {{\text{for}}\;m = 1,3,5, \cdots ,} \\ \end{array} $

where $ {\text{c}} \cdot {\text{e}}$ denotes the inner product of $ c$ and $ e$ the area of $ m$-dimensional unit sphere, and $ \chi (M)$ the Euler characteristic of $ M$.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53.72

Retrieve articles in all journals with MSC: 53.72


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0273541-X
PII: S 0002-9939(1971)0273541-X
Keywords: Closed hypersurface, differential form, Gauss-Kronecker curvature, Euler characteristic, Gauss-Bonnet-Grotemeyer formula
Article copyright: © Copyright 1971 American Mathematical Society