Ricci curvature of real hypersurfaces in complex hyperbolic space

Bang-Yen Chen

Archivum Mathematicum (2002)

  • Volume: 038, Issue: 1, page 73-80
  • ISSN: 0044-8753

Abstract

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First we prove a general algebraic lemma. By applying the algebraic lemma we establish a general inequality involving the Ricci curvature of an arbitrary real hypersurface in a complex hyperbolic space. We also classify real hypersurfaces with constant principal curvatures which satisfy the equality case of the inequality.

How to cite

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Chen, Bang-Yen. "Ricci curvature of real hypersurfaces in complex hyperbolic space." Archivum Mathematicum 038.1 (2002): 73-80. <http://eudml.org/doc/248926>.

@article{Chen2002,
abstract = {First we prove a general algebraic lemma. By applying the algebraic lemma we establish a general inequality involving the Ricci curvature of an arbitrary real hypersurface in a complex hyperbolic space. We also classify real hypersurfaces with constant principal curvatures which satisfy the equality case of the inequality.},
author = {Chen, Bang-Yen},
journal = {Archivum Mathematicum},
keywords = {Ricci curvature; shape operator; real hypersurface; algebraic lemma; tubular hypersurface; horosphere; complex hyperbolic space; Ricci curvature; shape operator; algebraic lemma; tubular hypersurface; horosphere; complex hyperbolic space},
language = {eng},
number = {1},
pages = {73-80},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Ricci curvature of real hypersurfaces in complex hyperbolic space},
url = {http://eudml.org/doc/248926},
volume = {038},
year = {2002},
}

TY - JOUR
AU - Chen, Bang-Yen
TI - Ricci curvature of real hypersurfaces in complex hyperbolic space
JO - Archivum Mathematicum
PY - 2002
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 038
IS - 1
SP - 73
EP - 80
AB - First we prove a general algebraic lemma. By applying the algebraic lemma we establish a general inequality involving the Ricci curvature of an arbitrary real hypersurface in a complex hyperbolic space. We also classify real hypersurfaces with constant principal curvatures which satisfy the equality case of the inequality.
LA - eng
KW - Ricci curvature; shape operator; real hypersurface; algebraic lemma; tubular hypersurface; horosphere; complex hyperbolic space; Ricci curvature; shape operator; algebraic lemma; tubular hypersurface; horosphere; complex hyperbolic space
UR - http://eudml.org/doc/248926
ER -

References

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  1. Real hypersurfaces with constant principal curvatures in complex hyperbolic space, J. Reine Angew. Math. 395 (1989), 132-141. (1989) Zbl0655.53046MR0983062
  2. Geometry of Submanifolds, M. Dekker, New York, 1973. MR0353212
  3. Some pinching and classification theorems for minimal submanifolds, Arch. Math. (Basel) 60 (1993), 568–578. (1993) Zbl0811.53060MR1216703
  4. A general inequality for submanifolds in complex-space-forms and its applications, Arch. Math. (Basel) 67 (1996), 519–528. (1996) Zbl0871.53043MR1418914
  5. Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimension, Glasgow Math. J. 41 (1999), 33-41. (1999) MR1689730
  6. The normal curvature of totally real submanifolds of S 6 ( 1 ) , Glasgow Math. J. 40 (1998), 199–204. (1998) MR1630238
  7. A pointwise inequality in submanifold theory, Arch. Math. (Brno) 35 (1999), 115–128. (1999) MR1711669

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