Abstract
We study classifying problems for real hypersurfaces in a complex two-plane Grassmannian G2(ℂm+2). In relation to the generalized Tanaka–Webster connection, we consider a new concept of parallel normal Jacobi operator for real hypersurfaces in G2(ℂm+2) and prove that a real hypersurface in G2(ℂm+2) with generalized Tanaka–Webster 𝔇⊥-parallel normal Jacobi operator is locally congruent to an open part of a tube around a totally geodesic quaternionic projective space ℍPn in G2(ℂm+2), where m = 2n.
Communicated by: P. Eberlein
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Funding: This research was supported by Basic Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2017R1A6A3A01012821) and the second author by grant Proj. No. NRF-2018-R1D1A1B-05040381 from the National Research Foundation of Korea.
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