Complete classification of spatial surfaces with parallel mean curvature vector in arbitrary non-flat pseudo-Riemannian space forms

• Autorzy: Bang-Yen Chen
• Języki publikacji: EN

Abstrakty

EN

Submanifolds with parallel mean curvature vector play important roles in differential geometry, theory of harmonic maps as well as in physics. Spatial surfaces in 4D Lorentzian space forms with parallel mean curvature vector were classified by B. Y. Chen and J. Van der Veken in [9]. Recently, spatial surfaces with parallel mean curvature vector in arbitrary pseudo-Euclidean spaces are also classified in [7]. In this article, we classify spatial surfaces with parallel mean curvature vector in pseudo-Riemannian spheres and pseudo-hyperbolic spaces with arbitrary codimension and arbitrary index. Consequently, we achieve the complete classification of spatial surfaces with parallel mean curvature vector in all pseudo-Riemannian space forms. As an immediate by-product, we obtain the complete classifications of spatial surfaces with parallel mean curvature vector in arbitrary Lorentzian space forms.

Słowa kluczowe

EN

Spatial surface; Parallel mean curvature vector; Lorentzian space form; Pseudo-Riemannian space form; CMC surface; Light cone

Kategorie tematyczne

• 83C15: Exact solutions
• 53C50: Lorentz manifolds, manifolds with indefinite metrics
• 53C40: Global submanifolds

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 3
• Strony: 400-428

Daty

wydano

2009-09-01

online

2009-08-12

Twórcy

autor

Bang-Yen Chen

• Michigan State University

Bibliografia

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• [2] Chen B.Y., On the surface with parallel mean curvature vector, Indiana Univ. Math. J., 1973, 22, 655–666 http://dx.doi.org/10.1512/iumj.1973.22.22053
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• [9] Chen B.Y., Van der Veken J., Complete classification of parallel surfaces in 4-dimensional Lorentzian space forms, Tohoku Math. J., 2009, 61, 1–40 http://dx.doi.org/10.2748/tmj/1238764545
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• [16] Verstraelen L., Pieters M., Some immersions of Lorentz surfaces into a pseudo-Riemannian space of constant curvature and of signature (2; 2), Rev. Roumaine Math. Pures Appl., 1976, 21, 593–600

Identyfikatory

DOI

10.2478/s11533-009-0020-9