1- https://doi.org/10.1063/1.1814734
On Einstein Lagrangian submanifolds of a complex projective space
- Jan 1, 2004
- AIP conference proceedings
- Yoshio Matsuyama
Abstract
In the present paper we study Einstein Lagrangian submanifolds. We show that if M is a complete Einstein Lagrangian minimal submanifold of a complex projective space CPn(c), then M is parallel and M is one of the following conditions holds: a) M is totally geodesic, b) n = 2 and M is a finite Riemannian covering of a torus minimally embedded in CP2(c) with parallel second fundamental form, c) n > 2 and M is an embedded submanifold congruent to the standard embedding of: SU(3)/SO(3),n = 5;SU(3),n = 8;SU(6)/Sp(3),n = 14 or E6/F4,n = 26. We also study a compact Einstein Kaehler submanifold of a complex projective space.
- # Einstein Lagrangian
- # Complex Projective Space
- # Complex Space
- # Present Paper
- # Lagrangian Submanifolds
- # Projective Space
