On an integral formula for closed hypersurfaces of the sphere
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- by Chorng-shi Houh PDF
- Proc. Amer. Math. Soc. 35 (1972), 234-237 Request permission
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.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- 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