Real hypersurfaces of non-flat complex space forms with two generalized conditions on the Jacobi structure operator
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Theoharis Theofanidis
Abstract
We aim to classify the real hypersurfaces M in a Kaehler complex space form Mn(c) satisfying the two conditions
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Communicated by: P. Eberlein
Acknowledgements
The author would like to express his sincere gratitude to the referee for his/ her well-established arguments, corrections and suggestions that improved significantly the contents of the current manuscript.
References
[1] J. Berndt, Real hypersurfaces with constant principal curvatures in complex hyperbolic space. J. Reine Angew. Math. 395 (1989), 132–141. MR983062 Zbl 0655.53046Search in Google Scholar
[2] D. E. Blair, Riemannian geometry of contact and symplectic manifolds. Birkhäuser Boston, Inc., Boston, MA 2002. MR1874240 Zbl 1011.53001Search in Google Scholar
[3] T. E. Cecil, P. J. Ryan, Focal sets and real hypersurfaces in complex projective space. Trans. Amer. Math. Soc. 269 (1982), 481–499. MR637703 Zbl 0492.53039Search in Google Scholar
[4] J. T. Cho, U.-H. Ki, Real hypersurfaces in complex space forms with Reeb flow symmetric structure Jacobi operator. Canad. Math. Bull. 51 (2008), 359–371. MR2436926 Zbl 1147.53016Search in Google Scholar
[5] T. A. Ivey, P. J. Ryan, Hopf hypersurfaces of small Hopf principal curvature in ℂℍ2 Geom. Dedicata 141 (2009), 147–161. MR2520069 Zbl 1177.53045Search in Google Scholar
[6] U.-H. Ki, H. Kurihara, Jacobi operators along the structure flow on real hypersurfaces in a nonflat complex space form II. Bull. Korean Math. Soc. 48 (2011), 1315–1327. MR2894899 Zbl 1239.53073Search in Google Scholar
[7] U.-H. Ki, S. Nagai, The Ricci tensor and structure Jacobi operator of real hypersurfaces in a complex projective space. J. Geom. 94 (2009), 123–142. MR2534413 Zbl 1177.53055Search in Google Scholar
[8] U.-H. Ki, J. D. D. Pérez, F. G. Santos, Y. J. Suh, Real hypersurfaces in complex space forms with ξ-parallel Ricci tensor and structure Jacobi operator. J. Korean Math. Soc. 44 (2007), 307–326. MR2295391 Zbl 1144.53069Search in Google Scholar
[9] M. Kimura, Real hypersurfaces and complex submanifolds in complex projective space. Trans. Amer. Math. Soc. 296 (1986), 137–149. MR837803 Zbl 0597.53021Search in Google Scholar
[10] S. Maeda, Geometry of the horosphere in a complex hyperbolic space. Differential Geom. Appl. 29 (2011), S246–S250. MR2832025 Zbl 1225.53056Search in Google Scholar
[11] S. Montiel, A. Romero, On some real hypersurfaces of a complex hyperbolic space. Geom. Dedicata 20 (1986), 245–261. MR833849 Zbl 0587.53052Search in Google Scholar
[12] R. Niebergall, P. J. Ryan, Real hypersurfaces in complex space forms. In: Tight and taut submanifolds Berkeley, CA, 1994), volume 32 of Math. Sci. Res. Inst. Publ., 233–305, Cambridge Univ. Press 1997. MR1486875 Zbl 0904.53005Search in Google Scholar
[13] M. Okumura, On some real hypersurfaces of a complex projective space. Trans. Amer. Math. Soc. 212 (1975), 355–364. MR377787 Zbl 0288.53043Search in Google Scholar
[14] R. Takagi, On homogeneous real hypersurfaces in a complex projective space. Osaka Math. J. 10 (1973), 495–506. MR336660 Zbl 0274.53062Search in Google Scholar
[15] R. Takagi, Real hypersurfaces in a complex projective space with constant principal curvatures. J. Math. Soc. Japan 27 (1975), 43–53. MR355906 Zbl 0292.53042Search in Google Scholar
[16] T. Theofanidis, Real hypersurfaces of non-flat complex space forms with generalized ξ-parallel Jacobi structure operator. Glasg. Math. J. 58 (2016), 677–687. MR3530493 Zbl 1354.53068Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- On vector bundles over reducible curves with a node
- Inscribed rectangle coincidences
- 𝔽p2-maximal curves with many automorphisms are Galois-covered by the Hermitian curve
- Tetrahedral cages for unit discs
- When is M0,n(ℙ1,1) a Mori dream space?
- Rank-one isometries of CAT(0) cube complexes and their centralisers
- Wall-crossing in genus-zero hybrid theory
- The curve Yn = Xℓ(Xm + 1) over finite fields II
- Uniqueness results for bodies of constant width in the hyperbolic plane
- A note on large Kakeya sets
- On static manifolds and related critical spaces with cyclic parallel Ricci tensor
- The motivic Igusa zeta function of a space monomial curve with a plane semigroup
- Real hypersurfaces of non-flat complex space forms with two generalized conditions on the Jacobi structure operator
