Homogeneous symplectic manifolds with Ricci-type curvature

✍ Scribed by M. Cahen; S. Gutt; J. Horowitz; J. Rawnsley

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 83 KB
• Volume: 38
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(00)00058-9

✦ Synopsis

We consider invariant symplectic connections ∇ on homogeneous symplectic manifolds (M, ω) with curvature of Ricci type. Such connections are solutions of a variational problem studied by Bourgeois and Cahen, and provide an integrable almost complex structure on the bundle of almost complex structures compatible with the symplectic structure. If M is compact with finite fundamental group then (M, ω) is symplectomorphic to P n (C) with a multiple of its Kähler form and ∇ is affinely equivalent to the Levi-Civita connection.