Classification of minimal Lorentz surfaces in indefinite space forms with arbitrary codimension and arbitrary index

• Autores: Bang-Yen Chen
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 78, Fasc. 2, 2011, págs. 485-503
• Idioma: inglés
• DOI: 10.5486/pmd.2011.4860
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• Resumen

  • Since J. L. Lagrange initiated in [18] the study of minimal surfaces of Euclidean 3-space in 1760, minimal surfaces in real space forms have been studied extensively by many mathematicians during the last two and half centuries. In contrast, so far very few results on minimal Lorentz surfaces in inde nite space forms are known. Hence, in this paper we investigate minimal Lorentz surfaces in arbitrary inde nite space forms. As a consequence, we obtain several classi cation results for minimal Lorentz surfaces in inde nite space forms. In particular, we completely classify all minimal Lorentz surfaces in a pseudo-Euclidean space Em s with arbitrary dimension m and arbitrary index s.