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Real Hypersurfaces in Complex Two-Plane Grassmannians with Recurrent Structure Jacobi Operator

  • Imsoon Jeong
  • Young Jin Suh
  • Changhwa Woo
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 106)

Abstract

In this paper, we introduce a new notion of recurrent structure Jacobi operator, that is, \((\nabla _{X}R_{\xi })Y =\omega (X)R_{\xi }Y\) for any tangent vector fields X and Y on a real hypersurface M in a complex two-plane Grassmannian, where R ξ denotes the structure Jacobi operator and ω a certain 1-form on M. Next, we prove that there does not exist any Hopf hypersurface M in a complex two-plane Grassmannian with recurrent structure Jacobi operator.

Keywords

Vector Field Real Hypersurface Shape Operator Hermitian Structure Hermitian Symmetric Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work was supported by Grant Proj. No. NRF-2011-220-C00002 from National Research Foundation of Korea. The first author is supported by grant Proj. No. NRF-2011-0013381, the second author by Grant Proj. No. NRF-2012-R1A2A2A01043023 and the third author supported by NRF Grant funded by the Korean Government (NRF-2013-Fostering Core Leaders of Future Basic Science Program).

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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Department of MathematicsKyungpook National UniversityDaeguKorea

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