On an inequality of Oprea for Lagrangian submanifolds
Franki Dillen; Johan Fastenakels
Open Mathematics (2009)
- Volume: 7, Issue: 1, page 140-144
- ISSN: 2391-5455
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topFranki Dillen, and Johan Fastenakels. "On an inequality of Oprea for Lagrangian submanifolds." Open Mathematics 7.1 (2009): 140-144. <http://eudml.org/doc/269770>.
@article{FrankiDillen2009,
abstract = {We show that a Lagrangian submanifold of a complex space form attaining equality in the inequality obtained by Oprea in [8], must be totally geodesic.},
author = {Franki Dillen, Johan Fastenakels},
journal = {Open Mathematics},
keywords = {Curvature inequalities; Lagrangian submanifolds; curvature inequalities},
language = {eng},
number = {1},
pages = {140-144},
title = {On an inequality of Oprea for Lagrangian submanifolds},
url = {http://eudml.org/doc/269770},
volume = {7},
year = {2009},
}
TY - JOUR
AU - Franki Dillen
AU - Johan Fastenakels
TI - On an inequality of Oprea for Lagrangian submanifolds
JO - Open Mathematics
PY - 2009
VL - 7
IS - 1
SP - 140
EP - 144
AB - We show that a Lagrangian submanifold of a complex space form attaining equality in the inequality obtained by Oprea in [8], must be totally geodesic.
LA - eng
KW - Curvature inequalities; Lagrangian submanifolds; curvature inequalities
UR - http://eudml.org/doc/269770
ER -
References
top- [1] Bolton J., Dillen F., Fastenakels J., Vrancken L., A best possible inequality for curvature-like tensor fields, preprint Zbl1175.53023
- [2] Bolton J., Rodriguez Montealegre C., Vrancken L., Characterizing warped product Lagrangian immersions in complex projective space, Proc. Edinb. Math. Soc., 2008, 51, 1–14 [WoS]
- [3] Bolton J., Vrancken L., Lagrangian submanifolds attaining equality in the improved Chen’s inequality, Bull. Belg. Math. Soc., 2007, 14, 311–315 Zbl1130.53016
- [4] Chen B.Y., Some pinching and classification theorems for minimal submanifolds, Arch. Math., 1993, 60, 568–578 http://dx.doi.org/10.1007/BF01236084[Crossref] Zbl0811.53060
- [5] Chen B.Y., Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimension, Glasgow Math. J., 1999, 41, 33–41 http://dx.doi.org/10.1017/S0017089599970271[Crossref] Zbl0962.53015
- [6] Chen B.Y., Riemannian geometry of Lagrangian submanifolds, Taiwan. J. Math., 2001, 5, 681–723 Zbl1002.53053
- [7] Oprea T., Chen’s inequality in Lagrangian case, Colloq. Math., 2007, 108, 163–169 http://dx.doi.org/10.4064/cm108-1-15[Crossref] Zbl1118.53035
- [8] Oprea T., On a Riemannian invariant of Chen type, Rocky Mountain J. Math., 2008, 38, 567–581 http://dx.doi.org/10.1216/RMJ-2008-38-2-567[Crossref] Zbl1195.53072
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