PORTUGALIAE MATHEMATICA Vol. 60, No. 2, pp. 215235 (2003) 

On the Kähler Angles of SubmanifoldsIsabel M. C. SalavessaCentro de Física das Interacçoes Fundamentais, Instituto Superior Técnico,Edifício Ciência, Piso 3, 1049001 Lisboa  PORTUGAL Email: isabel@cartan.ist.utl.pt Abstract: We prove that under certain conditions on the mean curvature and on the Kähler angles, a compact submanifold $M$ of real dimension $2n$, immersed into a KählerEinstein manifold $N$ of complex dimension $2n$, must be either a complex or a Lagrangian submanifold of $N$, or have constant Kähler angle, depending on $n=1$, $n=2$, or $n\geq 3$, and the sign of the scalar curvature of $N$. These results generalize to nonminimal submanifolds some known results for minimal submanifolds. Our main tool is a Bochnertype technique involving a formula on the Laplacian of a symmetric function on the Kähler angles and the Weitzenböck formula for the Kähler form of $N$ restricted to $M$. Keywords: Lagrangian submanifold; KählerEinstein manifold; Kähler angles. Classification (MSC2000): 53C42.; 53C21, 53C55, 53C40. Full text of the article:
Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.
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