Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 35 (1994), No. 1, 55-66.
The Cubic Representation of a Submanifold
Bang-yen Chen, Wei-Eihn Kuan
Abstract.
Let $f:M\rightarrow E^m$ be an immersion of a
manifold in a Euclidean space. Then the tensor product map $f^3:=f\x f\x
f:M \rightarrow E^m\x E^m\x E^m\cong E^{m^3}$ is called the cubic
representation of the submanifold. The purpose of this article
is to investigate the geometry of the cubic representation of a
spherical submanifold. Several theorems in this respect are
obtained.
MSC 1991: 53C40, 53B25