Geometric properties of Lie hypersurfaces in a complex hyperbolic space

Young Ho Kim; Sadahiro Maeda; Hiromasa Tanabe

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 4, page 983-996
  • ISSN: 0011-4642

Abstract

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We study homogeneous real hypersurfaces having no focal submanifolds in a complex hyperbolic space. They are called Lie hypersurfaces in this space. We clarify the geometry of Lie hypersurfaces in terms of their sectional curvatures, the behavior of the characteristic vector field and their holomorphic distributions.

How to cite

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Kim, Young Ho, Maeda, Sadahiro, and Tanabe, Hiromasa. "Geometric properties of Lie hypersurfaces in a complex hyperbolic space." Czechoslovak Mathematical Journal 69.4 (2019): 983-996. <http://eudml.org/doc/294532>.

@article{Kim2019,
abstract = {We study homogeneous real hypersurfaces having no focal submanifolds in a complex hyperbolic space. They are called Lie hypersurfaces in this space. We clarify the geometry of Lie hypersurfaces in terms of their sectional curvatures, the behavior of the characteristic vector field and their holomorphic distributions.},
author = {Kim, Young Ho, Maeda, Sadahiro, Tanabe, Hiromasa},
journal = {Czechoslovak Mathematical Journal},
keywords = {complex hyperbolic space; homogeneous real hypersurface; Lie hypersurface; homogeneous ruled real hypersurface; equidistant hypersurface; horosphere; sectional curvature; shape operator; integral curve of the characteristic vector field; holomorphic distributions; homogeneous curve},
language = {eng},
number = {4},
pages = {983-996},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Geometric properties of Lie hypersurfaces in a complex hyperbolic space},
url = {http://eudml.org/doc/294532},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Kim, Young Ho
AU - Maeda, Sadahiro
AU - Tanabe, Hiromasa
TI - Geometric properties of Lie hypersurfaces in a complex hyperbolic space
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 4
SP - 983
EP - 996
AB - We study homogeneous real hypersurfaces having no focal submanifolds in a complex hyperbolic space. They are called Lie hypersurfaces in this space. We clarify the geometry of Lie hypersurfaces in terms of their sectional curvatures, the behavior of the characteristic vector field and their holomorphic distributions.
LA - eng
KW - complex hyperbolic space; homogeneous real hypersurface; Lie hypersurface; homogeneous ruled real hypersurface; equidistant hypersurface; horosphere; sectional curvature; shape operator; integral curve of the characteristic vector field; holomorphic distributions; homogeneous curve
UR - http://eudml.org/doc/294532
ER -

References

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  1. Adachi, T., Bao, T., Maeda, S., 10.14492/hokmj/1392906097, Hokkaido Math. J. 43 (2014), 137-150. (2014) Zbl1288.53045MR3178483DOI10.14492/hokmj/1392906097
  2. Berndt, J., 10.1007/PL00004673, Math. Z. 229 (1998), 589-600. (1998) Zbl0929.53025MR1664778DOI10.1007/PL00004673
  3. Berndt, J., Tamaru, H., 10.1090/S0002-9947-07-04305-X, Trans. Am. Math. Soc. 359 (2007), 3425-3438. (2007) Zbl1117.53041MR2299462DOI10.1090/S0002-9947-07-04305-X
  4. Chen, B.-Y., Maeda, S., 10.3836/tjm/1255958318, Tokyo J. Math. 24 (2001), 133-152. (2001) Zbl1015.53039MR1844424DOI10.3836/tjm/1255958318
  5. Hamada, T., Hoshikawa, Y., Tamaru, H., 10.1007/s00022-012-0127-1, J. Geom. 103 (2012), 247-261. (2012) Zbl1266.53057MR2995128DOI10.1007/s00022-012-0127-1
  6. Kimura, M., Maeda, S., 10.1007/BF01159962, Math. Z. 202 (1989), 299-311. (1989) Zbl0661.53015MR1017573DOI10.1007/BF01159962
  7. Kon, S. H., Loo, T.-H., 10.1007/s00209-010-0715-4, Math. Z. 269 (2011), 47-58. (2011) Zbl1227.53071MR2836059DOI10.1007/s00209-010-0715-4
  8. Lohnherr, M., Reckziegel, H., 10.1023/A:1005000122427, Geom. Dedicata 74 (1999), 267-286. (1999) Zbl0932.53018MR1669351DOI10.1023/A:1005000122427
  9. Maeda, S., 10.1016/j.difgeo.2011.04.048, Differ. Geom. Appl. 29 (2011), s246--s250. (2011) Zbl1225.53056MR2832025DOI10.1016/j.difgeo.2011.04.048
  10. Maeda, S., Adachi, T., 10.1090/S0002-9939-97-03627-7, Proc. Am. Math. Soc. 125 (1997), 1197-1202. (1997) Zbl0876.53045MR1353391DOI10.1090/S0002-9939-97-03627-7
  11. Maeda, S., Adachi, T., Kim, Y. H., 10.2969/jmsj/06110315, J. Math. Soc. Japan 61 (2009), 315-325. (2009) Zbl1159.53012MR2272881DOI10.2969/jmsj/06110315
  12. Maeda, S., Ohnita, Y., 10.1007/BF02424315, Geom. Dedicata 30 (1989), 93-114. (1989) Zbl0669.53042MR0995941DOI10.1007/BF02424315
  13. Maeda, S., Tanabe, H., 10.1007/s00013-015-0839-1, Arch. Math. 105 (2015), 593-599. (2015) Zbl1329.53032MR3422863DOI10.1007/s00013-015-0839-1
  14. Niebergall, R., Ryan, P. J., Real hypersurfaces in complex space forms, Tight and Taut Submanifolds. Based on the Workshop on Differential Systems, Submanifolds and Control Theory, Berkeley, CA, USA, 1994 Math. Sci. Res. Inst. Publ. 32, Cambridge University Press, Cambridge (1997), 233-305. (1997) Zbl0904.53005MR1486875

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