Maslov class and minimality in Calabi–Yau manifolds

✍ Scribed by Alessandro Arsie

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 85 KB
• Volume: 35
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(00)00003-6

✦ Synopsis

Generalizing the construction of the Maslov class [µ ] for a Lagrangian embedding in a symplectic vector space, we prove that it is possible to give a consistent definition of the class [µ ] for any Lagrangian submanifold of a Calabi-Yau manifold. Moreover, extending a result of Morvan in symplectic vector spaces, we prove that [µ ] can be represented by i H ω, where H is the mean curvature vector field of the Lagrangian embedding and ω is the Kähler form associated to the Calabi-Yau metric. Finally, we conjecture a generalization of the Maslov class for Lagrangian submanifolds of any symplectic manifold via the mean curvature representation.