By using the notion of Fischer–Marsden equation on real hypersurfaces in the complex hyperbolic quadric Q^(m∗)=SO^(o)_(2,m)/SO_(2)SO_(m),we can assert that there does not exist a non-trivial solution(g,ν)of Fischer...By using the notion of Fischer–Marsden equation on real hypersurfaces in the complex hyperbolic quadric Q^(m∗)=SO^(o)_(2,m)/SO_(2)SO_(m),we can assert that there does not exist a non-trivial solution(g,ν)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,ν)of the Fischer–Marsden 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∗).展开更多
We introduce a new notion of pseudo-anti commuting Ricci tensor for real hypersurfaces in the noncompact complex hyperbolic quadric Q^(m?)= SO_2~0,_m/SO_2SO_m and give a complete classi?cation of these hypersurfaces.
基金supported by Grants Proj.No.NRF-2018-R1D1A1B-05040381&NRF-2021-R1C1C-2009847 from National Research Foundation of Korea.
文摘By using the notion of Fischer–Marsden equation on real hypersurfaces in the complex hyperbolic quadric Q^(m∗)=SO^(o)_(2,m)/SO_(2)SO_(m),we can assert that there does not exist a non-trivial solution(g,ν)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,ν)of the Fischer–Marsden 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∗).
基金supported by National Research Foundation of Korea (Grant No. NRF2015-R1A2A1A-01002459)
文摘We introduce a new notion of pseudo-anti commuting Ricci tensor for real hypersurfaces in the noncompact complex hyperbolic quadric Q^(m?)= SO_2~0,_m/SO_2SO_m and give a complete classi?cation of these hypersurfaces.
