Startseite đ”‡âŠ„-parallel normal Jacobi operators for Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka–Webster connection
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đ”‡âŠ„-parallel normal Jacobi operators for Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka–Webster connection

  • Eunmi Pak EMAIL logo und Young Jin Suh
Veröffentlicht/Copyright: 4. Juli 2019
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Advances in Geometry
Aus der Zeitschrift Advances in Geometry Band 20 Heft 2

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 đ”‡âŠ„-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.

Keywords: Real hypersurface; complex two-plane Grassmannian; Hopf hypersurface; generalized Tanaka–Webster connection; normal Jacobi operator; generalized Tanaka–Webster parallel normal Jacobi operator
MSC 2010: Primary 53C40; Secondary 53C15

  1. Communicated by: P. Eberlein

  2. 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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Received: 2017-03-06
Revised: 2018-03-10
Published Online: 2019-07-04
Published in Print: 2020-04-28

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. On the order sequence of an embedding of the Ree curve
  3. đ”‡âŠ„-parallel normal Jacobi operators for Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka–Webster connection
  4. A Krasnosel’skii-type theorem for certain orthogonal polytopes starshaped via k-staircase paths
  5. Higher algebraic structures in Hamiltonian Floer theory
  6. Additive structures on f-vector sets of polytopes
  7. The degree of the tangent and secant variety to a projective surface
  8. Building lattices and zeta functions
  9. Quaternionic equiangular lines
  10. Non-reduced moduli spaces of sheaves on multiple curves
https://doi.org/10.1515/advgeom-2019-0012
Schlagwörter fĂŒr diesen Artikel
Real hypersurface; complex two-plane Grassmannian; Hopf hypersurface; generalized Tanaka–Webster connection; normal Jacobi operator; generalized Tanaka–Webster parallel normal Jacobi operator

Artikel in diesem Heft

  1. Frontmatter
  2. On the order sequence of an embedding of the Ree curve
  3. đ”‡âŠ„-parallel normal Jacobi operators for Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka–Webster connection
  4. A Krasnosel’skii-type theorem for certain orthogonal polytopes starshaped via k-staircase paths
  5. Higher algebraic structures in Hamiltonian Floer theory
  6. Additive structures on f-vector sets of polytopes
  7. The degree of the tangent and secant variety to a projective surface
  8. Building lattices and zeta functions
  9. Quaternionic equiangular lines
  10. Non-reduced moduli spaces of sheaves on multiple curves
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