具有广义Tanaka-Webster reeb -平行结构Jacobi算子的复两平面Grassmannians的Hopf超曲面

Pub Date : 2019-09-23 DOI:10.5666/KMJ.2019.59.3.525

Byung-Hak Kim, Hyunjin Lee, Eunmi Pak

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引用次数: 1

摘要

关于广义Tanaka-Webster连接，我们考虑了复两平面Grassmannian G2(m+2)上实超曲面的\(\mathfrak{D}^ \bot\) -平行结构Jacobi算子的新概念，并证明了具有广义Tanaka-Webster \(\mathfrak{D}^ \bot\) -平行结构Jacobi算子的G2(m+2)上的实超曲面局部同于G2(m+2)上的全测地四元数投影空间Pn周围的一个管的开口部分，其中m = 2n。

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Hopf Hypersurfaces in Complex Two-plane Grassmannians with Generalized Tanaka-Webster Reeb-parallel Structure Jacobi Operator

Regarding the generalized Tanaka-Webster connection, we considered a new notion of \(\mathfrak{D}^ \bot\)-parallel structure Jacobi operator for a real hypersurface in a complex two-plane Grassmannian G2(ℂm+2) and proved that a real hypersurface in G2(ℂm+2) with generalized Tanaka-Webster \(\mathfrak{D}^ \bot\)-parallel structure 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.

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