Fischer-Marsden conjecture for hypersurfaces of the complex hyperbolic space

초록

In this paper, we want to solve the Fischer-Marsden conjecture on real hypersurfaces in the complex hyperbolic space CHn = SU1,n/S(U1Un). First we prove that it is true on hypersurfaces with isometric Reeb flow in CHn. Next it is also true on a certain class of contact hypersurfaces in CHn. That is, we have shown that there does not exist a non-trivial solution (g, nu) of Fischer-Marsden equation on contact real hypersurfaces with radius r is an element of[r(1), infinity), where coth(2r(1)) = root 2n-3/n-2 , in the complex hyperbolic space CHn. Consequently, the Fischer-Marsden conjecture is true on these two kinds of real hypersurfaces in the complex hyperbolic space CHn. (c) 2023 Elsevier B.V. All rights reserved.

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