Global Differential Geometry and Global Analysis pp 140-144 | Cite as
A generalization of Weyl’s tube formula
Conference paper
First Online:
Keywords
Riemannian Manifold Comparison Theorem Tensor Field Geodesic Ball Compact Closure
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- [AL]C.B. Allendoerfer, "The Euler number of a Riemannian manifold," Amer. J. Math. 62 (1940), 243–248.MathSciNetCrossRefMATHGoogle Scholar
- [AW]C.B. Allendoerfer and A. Weil, "The Gauss-Bonnet theorem for Riemannian polyhedra," Trans. Amer. Math. Soc. 53 (1943), 101–129.MathSciNetCrossRefMATHGoogle Scholar
- [BI]R. Bishop, "A relation between volume, mean curvature, and diameter," Amer. Math. Soc. Notices 10 (1963), 364.Google Scholar
- [BU]S.V. Buyalo, "An extremal theorem of Riemannian geometry," Math. Notes 19 (1978), 468–473. Translated from Mat. Zametki 19 (1976), 795–804.CrossRefGoogle Scholar
- [GV1]A. Gray and L. Vanhecke, "The volumes of tubes about curves in a Riemannian manifold," Proc. London Math. Soc., to appear.Google Scholar
- [GV2]A. Gray and L. Vanhecke, "The volume of tubes in a Riemannian manifold," to appear.Google Scholar
- [GU]P. Günther, "Einige Sätze über das volumenelement eines Riemannschen Raumes," Publ. Math. Debrecen 7 (1960), 78–93.MathSciNetMATHGoogle Scholar
- [HK]E. Heintze and H. Karcher, "A general comparison theorem with applications to volume estimates for submanifolds," Ann. Sci. École Norm. Sup. (4) 11 (1978), 451–470.MathSciNetMATHGoogle Scholar
- [WY]H. Weyl, "On the volume of tubes," Amer. J. Math. 61 (1939), 461–472.MathSciNetCrossRefMATHGoogle Scholar
Copyright information
© Springer-Verlag 1981