Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-26T02:51:20.139Z Has data issue: false hasContentIssue false
  • English
  • Français

An integral formula for compact hypersurfaces in a Euclidean space and its applications

Published online by Cambridge University Press:  18 May 2009

Sharief Deshmukh
Sharief Deshmukh
Affiliation:
Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let M be a compact hypersurface in a Euclidena space ℝn+1. The support function p of M is the component of the position vector field of Min ℝn+1 along the unit normal vector field to M, which is a smooth function defined on M. Let S be the scalar curvature of M. The object of the present paper is to prove the following theorems.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 3 , September 1992 , pp. 309 - 311
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

REFERENCES

1.Coghlan, L. and Itokawa, Y., On the sectional curvature of compact hypersurfaces, Proc. Amer. Math. Soc. 109(1) (1990), 215–221.CrossRefGoogle Scholar
2.Jacobowitz, H., Isometric embedding of a compact Riemannian manifold into Euclidean space, Proc. Amer. Math. Soc. 40(1) (1973), 245–246.CrossRefGoogle Scholar
3.Kobayashi, S. and Nomizu, K., Foundations of differential geometry vol. II (Interscience Publ., 1969).Google Scholar