A GEOMETRIC CHARACTERIZATION OF THE WHITN EY SPHERE

Authors
BORRELLI V CHEN BY MORVAN JM
Citation
V. Borrelli et al., A GEOMETRIC CHARACTERIZATION OF THE WHITN EY SPHERE, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 321(11), 1995, pp. 1485-1490
Citations number
6
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
321
Issue
11
Year of publication
1995
Pages
1485 - 1490
Database
ISI
SICI code
0764-4442(1995)321:11<1485:AGCOTW>2.0.ZU;2-J
Abstract
We prove that the local geometrical invariants of a Lagrangian submani fold of C-n (the square of its mean curvature H-2 and its scalar curva ture tau), satisfy the following fundamental inequality: H-2 greater t han or equal to 2(n+2)/n(2)(n-1)tau. (We use for this purpose a partic ular property of symmetry of the second fundamental form of Lagrangian immersions.) The equality case allows to characterise the Whitney imm ersion.