Real hypersurfaces in the complex quadric with parallel structure Jacobi operator

preprint2016arXivOpen access

Abstract

First we introduce the notion of parallel structure Jacobi operator for real hypersurfaces in the complex quadric Qm=SOm+2/SOmSO2Q^m = SO_{m+2}/SO_mSO_2 . Next we give a complete classification of real hypersurfaces in Qm=SOm+2/SOmSO2Q^m = SO_{m+2}/SO_mSO_2 with parallel structure Jacobi operator.

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