On an inequality of Oprea for Lagrangian submanifolds

• Autorzy: Franki Dillen , Johan Fastenakels
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Curvature inequalities; Lagrangian submanifolds

Kategorie tematyczne

• 53B25: Local submanifolds

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 1
• Strony: 140-144

Daty

wydano

2009-03-01

online

2009-01-10

Twórcy

autor

Franki Dillen

• Department of Mathematics, Katholieke Universiteit Leuven, Leuven, Belgium

autor

Johan Fastenakels

• Department of Mathematics, Katholieke Universiteit Leuven, Leuven, Belgium

Bibliografia

• [1] Bolton J., Dillen F., Fastenakels J., Vrancken L., A best possible inequality for curvature-like tensor fields, preprint
• [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
• [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]
• [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]
• [6] Chen B.Y., Riemannian geometry of Lagrangian submanifolds, Taiwan. J. Math., 2001, 5, 681–723
• [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]
• [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]

Identyfikatory

DOI

10.2478/s11533-008-0064-2