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.
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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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Jeong, I., Suh, Y.J., Woo, C. (2014). Real Hypersurfaces in Complex Two-Plane Grassmannians with Recurrent Structure Jacobi Operator. In: Suh, Y.J., Berndt, J., Ohnita, Y., Kim, B.H., Lee, H. (eds) Real and Complex Submanifolds. Springer Proceedings in Mathematics & Statistics, vol 106. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55215-4_23
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DOI: https://doi.org/10.1007/978-4-431-55215-4_23
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