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Existence and Uniqueness Theorem for Slant Immersions and Its Applications

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Abstract

A slant immersion is an isometric immersion from a Riemannian manifold into an almost Hermitian manifold with constant Wirtinger angle. In this paper we establish the existence and uniqueness theorem for slant immersions into complex-space-forms. By applying this result, we prove in this paper several existence and nonexistence theorems for slant immersions. In particular, we prove the existence theorems for slant surfaces with prescribed mean curvature or with prescribed Gaussian curvature. We also prove the non-existence theorem for flat minimal proper slant surfaces in non-flat complex space forms.

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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, East Lansing, Michigan, 48824-1027, USA

    Bang-yen Chen

  2. Departement Wiskunde, Celestijnenlaan 200 B, B-3001, Leuven, Belgium

    Luc Vrancken

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  1. Bang-yen Chen
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  2. Luc Vrancken
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Correspondence to Bang-yen Chen.

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Chen, By., Vrancken, L. Existence and Uniqueness Theorem for Slant Immersions and Its Applications. Results. Math. 31, 28–39 (1997). https://doi.org/10.1007/BF03322149

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  • DOI: https://doi.org/10.1007/BF03322149

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