Fischer-Marsden Conjecture on Hypersurfaces in the Complex Projective

초록

By using the notion of Fischer-Marsden equation on real hypersurfaces in the complex projective space CPn = SUn+1/S(U1Un), we can assert that there does not exist a nontrivial solution (g, nu) of such equation if the real hypersurface has isometric Reeb flow. Next, as an application we also show that there does not exist a nontrivial solution (g, nu) of the Fischer-Marsden equation on contact real hypersurfaces except when the radius r(1) is an element of (0, r(0)) for a tube over a real projective space RP(n )in the complex projective space CPn. Consequently, the Fischer-Marsden conjecture is true on these two kinds of real hypersurfaces in the complex projective space CPn.

키워드