Fischer-Marsden Conjecture and Equation in the Complex Hyperbolic Quadric

초록

By using the notion of Fischer-Marsden equation on real hypersurfaces in the complex hyperbolic quadric Q(m*) = SO2.mo/SO2SOm, we can assert that there does not exist a non-trivial solution (g,.) of Fischer-Marsden equation on real hypersurfaces with isometric Reeb flow in the complex hyperbolic quadric Q(m*). Next, as an application we also show that there does not exist a non-trivial solution (g,.) of the FischerMarsden equation on contact real hypersurfaces in the complex hyperbolic quadric Q(m*). Consequently, the Fischer-Marsden conjecture is true on these two kinds of real hypersurfaces in the complex hyperbolic quadric Q(m*).

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