Differential geometry of tensor product immersions II
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 ofℓ-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 wordsType number tensor product immersion submanifolds of finite type Veronese immersion
MSC 199153 C 40 53 B 25 58 G 25
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- Chen, B.Y.:Total mean curvature and submanifolds of finite type. World Scientific, 1984.Google Scholar
- Chen, B.Y.: Differential geometry of tensor product immersions.Ann. Global Anal. Geom. 11 (1993), 345–359.Google Scholar
- 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
- Decruyenaere, F.;Dillen, F.;Verstraelen, L.;Vrancken, L.:The semiring of immersions of Riemannian manifolds. To appear in:Beiträge Algebra Geom.Google Scholar
- Houh, C.S.: Pseudo-umbilical surfaces with parallel second fundamental form.Tensor (N.S.) 26 (1972), 262–266.Google Scholar
- Yano, K.;Chen, B.Y.: Minimal submanifolds of a higher dimensional sphere.Tensor (N.S.) 22 (1971), 369–373.Google Scholar