Acknowledgement
The first author was supported by grant Proj. No. NRF-2019-R1I1A1A-01050300 and the second author by grant Proj. No. NRF-2018-R1D1A1B-05040381 from National Research Foundation of Korea.
References
- J. Berndt and Y. J. Suh, Real hypersurfaces with isometric Reeb flow in complex two-plane Grassmannians, Monatsh. Math. 137 (2002), no. 2, 87-98. https://doi.org/10.1007/s00605-001-0494-4
- J. Berndt and Y. J. Suh, Real hypersurfaces with isometric Reeb flow in complex quadrics, Internat. J. Math. 24 (2013), no. 7, 1350050, 18 pp. https://doi.org/10.1142/S0129167X1350050X
- J. Berndt and Y. J. Suh, Contact hypersurfaces in Kahler manifolds, Proc. Amer. Math. Soc. 143 (2015), no. 6, 2637-2649. https://doi.org/10.1090/S0002-9939-2015-12421-5
- A. L. Besse, Einstein Manifolds, reprint of the 1987 edition, Classics in Mathematics, Springer-Verlag, Berlin, 2008.
- S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, corrected reprint of the 1978 original, Graduate Studies in Mathematics, 34, American Mathematical Society, Providence, RI, 2001. https://doi.org/10.1090/gsm/034
- I. Jeong, H. Lee, and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians whose structure Jacobi operator is of Codazzi type, Acta Math. Hungar. 125 (2009), no. 1-2, 141-160. https://doi.org/10.1007/s10474-009-8245-4
- I. Jeong, J. D. P'erez, and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with parallel structure Jacobi operator, Acta Math. Hungar. 122 (2009), no. 1-2, 173-186. https://doi.org/10.1007/s10474-008-8004-y
- I. Jeong, Y. J. Suh, and C. Woo, Real hypersurfaces in complex two-plane Grassmannians with recurrent structure Jacobi operator, in Real and Complex Submanifolds, 267-278, Springer Proc. Math. Stat., 106, Springer, Tokyo, 2014. https://doi.org/10. 1007/978-4-431-55215-4_23
- U.-H. Ki, J. D. P'erez, F. G. Santos, and Y. J. Suh, Real hypersurfaces in complex space forms with ξ-parallel Ricci tensor and structure Jacobi operator, J. Korean Math. Soc. 44 (2007), no. 2, 307-326. https://doi.org/10.4134/JKMS.2007.44.2.307
- S. Klein, Totally geodesic submanifolds of the complex quadric, Differential Geom. Appl. 26 (2008), no. 1, 79-96. https://doi.org/10.1016/j.difgeo.2007.11.004
- A. W. Knapp, Lie Groups Beyond an Introduction, second edition, Progress in Mathematics, 140, Birkhauser Boston, Inc., Boston, MA, 2002.
- S. Kobayashi and K. Nomizu, Foundations of Differential Geometry. Vol. II, reprint of the 1969 original, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1996.
- H. Lee, J. D. P'erez, and Y. J. Suh, Derivatives of normal Jacobi operator on real hypersurfaces in the complex quadric, Bull. London Math. Soc. 52 (2020), 1122-1133. http://doi.org/10.1112/blms.12386
- H. Lee and Y. J. Suh, Real hypersurfaces with recurrent normal Jacobi operator in the complex quadric, J. Geom. Phys. 123 (2018), 463-474. https://doi.org/10.1016/j.geomphys.2017.10.003
- M. Okumura, On some real hypersurfaces of a complex projective space, Trans. Amer. Math. Soc. 212 (1975), 355-364. https://doi.org/10.2307/1998631
- J. D. Perez, On the structure vector field of a real hypersurface in complex quadric, Open Math. 16 (2018), no. 1, 185-189. https://doi.org/10.1515/math-2018-0021
- J. D. Perez, Commutativity of torsion and normal Jacobi operators on real hypersurfaces in the complex quadric, Publ. Math. Debrecen 95 (2019), no. 1-2, 157-168. https://doi.org/10.5486/pmd.2019.8424
- J. D. Perez and F. G. Santos, Real hypersurfaces in complex projective space with recurrent structure Jacobi operator, Differential Geom. Appl. 26 (2008), no. 2, 218-223. https://doi.org/10.1016/j.difgeo.2007.11.015
- J. D. Perez, F. G. Santos, and Y. J. Suh, Real hypersurfaces in complex projective space whose structure Jacobi operator is Lie ξ-parallel, Differential Geom. Appl. 22 (2005), no. 2, 181-188. https://doi.org/10.1016/j.difgeo.2004.10.005
- J. D. Perez and Y. J. Suh, Derivatives of the shape operator of real hypersurfaces in the complex quadric, Results Math. 73 (2018), no. 3, Paper No. 126, 10 pp. https://doi.org/10.1007/s00025-018-0888-4
- H. Reckziegel, On the geometry of the complex quadric, in Geometry and topology of submanifolds, VIII (Brussels, 1995/Nordfjordeid, 1995), 302-315, World Sci. Publ., River Edge, NJ, 1996.
- A. Romero, Some examples of indefinite complete complex Einstein hypersurfaces not locally symmetric, Proc. Amer. Math. Soc. 98 (1986), no. 2, 283-286. https://doi.org/10.2307/2045699
- A. Romero, On a certain class of complex Einstein hypersurfaces in indefinite complex space forms, Math. Z. 192 (1986), no. 4, 627-635. https://doi.org/10.1007/BF01162709
- B. Smyth, Differential geometry of complex hypersurfaces, Ann. of Math. (2) 85 (1967), 246-266. https://doi.org/10.2307/1970441
- Y. J. Suh, Real hypersurfaces in the complex quadric with Reeb parallel shape operator, Internat. J. Math. 25 (2014), no. 6, 1450059, 17 pp. https://doi.org/10.1142/S0129167X14500591
- Y. J. Suh, Real hypersurfaces in the complex quadric with Reeb invariant shape operator, Differential Geom. Appl. 38 (2015), 10-21. https://doi.org/10.1016/j.difgeo.2014.11.003
- Y. J. Suh, Real hypersurfaces in the complex quadric with parallel Ricci tensor, Adv. Math. 281 (2015), 886-905. https://doi.org/10.1016/j.aim.2015.05.012
- Y. J. Suh, Real hypersurfaces in the complex quadric with harmonic curvature, J. Math. Pures Appl. (9) 106 (2016), no. 3, 393-410. https://doi.org/10.1016/j.matpur.2016.02.015
- Y. J. Suh, Real hypersurfaces in the complex quadric with parallel structure Jacobi operator, Differential Geom. Appl. 51 (2017), 33-48. https://doi.org/10.1016/j.difgeo.2017.01.001
- Y. J. Suh and D. H. Hwang, Real hypersurfaces in the complex quadric with commuting Ricci tensor, Sci. China Math. 59 (2016), no. 11, 2185-2198. https://doi.org/10.1007/s11425-016-0067-7