Homogeneity of hypersurfaces in a sphere. (English) Zbl 0981.53040

Yamada, Akira

Tsukuba J. Math. 22, No. 1, 131-143 (1998).

From the introduction: In connection with I. M. Singer’s problem [Commun. Pure Appl. Math. 13, 685-697 (1960; Zbl 0171.42503)], we consider the homogeneity of hypersurfaces in \(S^{n+1}\) and prove the following Theorem A. Let \(M\) be an oriented closed hypersurface in \(S^{n+1}\) which is curvature homogeneous up to order 4. Then, \(M\) is homogeneous.

MSC:

53C40	Global submanifolds
53C30	Differential geometry of homogeneous manifolds

Keywords:

homogeneity; closed hypersurface; curvature homogeneous

Citations:

Zbl 0171.42503