Advertisement

Annals of Global Analysis and Geometry

, Volume 12, Issue 1, pp 87–96 | Cite as

Differential geometry of tensor product immersions II

  • Bang-Yen Chen
Article

Abstract

In the first part of this series, we prove that the tensor product immersionf1⊗⋯ ⊗f2k of2k isometric spherical immersions of a Riemannian manifoldM in Euclidean space is of-type withℓ ≥ k and classify tensor product immersionsf1⊗⋯⊗f2k which are ofk-type. In this article we investigate the tensor product immersionsf1⊗⋯⊗f2k which are of (k+1)-type. Several classification theorems are obtained.

Key words

Type number tensor product immersion submanifolds of finite type Veronese immersion 

MSC 1991

53 C 40 53 B 25 58 G 25 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Chen, B.Y.:Total mean curvature and submanifolds of finite type. World Scientific, 1984.Google Scholar
  2. [2]
    Chen, B.Y.: Differential geometry of tensor product immersions.Ann. Global Anal. Geom. 11 (1993), 345–359.Google Scholar
  3. [3]
    Chen, B.Y.;Ludden, G.D.: Surfaces with mean curvature vector parallel in the normal bundle.Nagoya Math. J. 47 (1972), 161–167.Google Scholar
  4. [4]
    Decruyenaere, F.;Dillen, F.;Verstraelen, L.;Vrancken, L.:The semiring of immersions of Riemannian manifolds. To appear in:Beiträge Algebra Geom.Google Scholar
  5. [5]
    Houh, C.S.: Pseudo-umbilical surfaces with parallel second fundamental form.Tensor (N.S.) 26 (1972), 262–266.Google Scholar
  6. [6]
    Yano, K.;Chen, B.Y.: Minimal submanifolds of a higher dimensional sphere.Tensor (N.S.) 22 (1971), 369–373.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Bang-Yen Chen
    • 1
  1. 1.Department of Mathematics MichiganState University East LansingMichiganUSA

Personalised recommendations