Abstract
From J-action point of views, slant surfaces are the simplest and the most natural surfaces of a (Lorentzian) Kähler surface (\( \tilde M,\tilde g \), J). Slant surfaces arise naturally and play some important roles in the studies of surfaces of Kähler surfaces (see, for instance, [13]). In this article, we classify quasi-minimal slant surfaces in the Lorentzian complex plane C 21 . More precisely, we prove that there exist five large families of quasi-minimal proper slant surfaces in C 21 . Conversely, quasi-minimal slant surfaces in C 21 are either Lagrangian or locally obtained from one of the five families. Moreover, we prove that quasi-minimal slant surfaces in a non-flat Lorentzian complex space form are Lagrangian.
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Dedicated to Professor Leopold Verstraelen on the occasion of his 60th birthday
This paper was written while the second author visited Michigan State University, supported by the grant from the Romanian Ministry of Education and Research. The second author would like to express his hearty thanks for the hospitality he received during this visit.
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Chen, B.Y., Mihai, I. Classification of quasi-minimal slant surfaces in Lorentzian complex space forms. Acta Math Hung 122, 307–328 (2009). https://doi.org/10.1007/s10474-008-8033-6
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DOI: https://doi.org/10.1007/s10474-008-8033-6