Fischer-Marsden conjecture on real hypersurfaces in the complex quadric

초록

By using the notion of Fischer-Marsden Equation on real hypersurfaces in the complex quadric Q(m)=SOm+2/SO2SOm, we can assert that there does not exist a non-trivial solution (g,v) of Fischer-Marsden Equation on real hypersurfaces with isometric Reeb flow in the complex quadric Q(m). Next as an application we also show that there does not exist a non-trivial solution (g,v) of the Fischer-Marsden Equation on contact real hypersurfaces in the complex quadric Q(m). Consequently, the Fischer-Marsden conjecture is true on these two kinds of real hypersurfaces in the complex quadric Q(m).

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