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ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On an integral formula for closed hypersurfaces of the sphere


Author: Chorng-shi Houh
Journal: Proc. Amer. Math. Soc. 35 (1972), 234-237
MSC: Primary 53C45
DOI: https://doi.org/10.1090/S0002-9939-1972-0296867-3
MathSciNet review: 0296867
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Abstract: In a compact oriented hypersurface $ {M^n}$ of the sphere $ {S^{n + 1}}$ the integral formula $ {\smallint _{{M^n}}}\nabla {K_r}dV = n{\smallint _{{M^n}}}({K_r}{K_1} - {K_{r + 1}})edV$ is proved where $ {K_r}$ is the rth mean curvature, e is the unit normal of $ {M^n}$ in $ {S^{n + 1}}$. Some applications are considered.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0296867-3
Keywords: Combined operation of the vector product, combined operation of the exterior product, principal curvatures, rth mean curvature, Stokes theorem
Article copyright: © Copyright 1972 American Mathematical Society

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