Fischer-Marsden conjecture on real hypersurfaces in the complex hyperbolic two-plane Grassmannians

초록

In this paper, the study of Fischer-Marsden equation on real hypersurfaces in the complex hyperbolic two-plane Grassmannian G(2)*(Cm+2) is first investigated. It is shown that there does not exist a non-trivial solution (g, rho) of Fischer-Marsden equation on real hypersurfaces with isometric Reeb flow in the complex hyperbolic two-plane Grassmannian G(2)*(Cm+2). Moreover, among the class of contact hypersurfaces in G(2)*(Cm+2), there exists a trivial solution (g, rho) of Fischer-Marsden equation on tubes with certain radii over the totally geodesic and totally real quaternionic hyperbolic space HHn in G(2)*(Cm+2). Consequently, the Fischer-Marsden [20] conjecture holds on the above tubes with certain radii in the complex hyperbolic two-plane Grassmannian G(2)*(Cm+2).

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