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A Liouville Theorem for the Complex Monge‐Ampère Equation on Product Manifolds
Author(s) -
Hein HansJoachim
Publication year - 2019
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21751
Subject(s) - mathematics , calabi–yau manifold , kähler manifold , automorphism , manifold (fluid mechanics) , product (mathematics) , bounded function , pure mathematics , constant (computer programming) , metric (unit) , mathematical analysis , geometry , mechanical engineering , operations management , computer science , engineering , economics , programming language
Let Y be a closed Calabi‐Yau manifold. Let ω be the Kähler form of a Ricci‐flat Kähler metric onℂ m × Y . We prove that if ω is uniformly bounded above and below by constant multiples ofω ℂ m+ ω Y , whereω ℂ mis the standard flat Kähler form onℂ mand ω Y is any Kähler form on Y , then ω is a product Kähler form up to a certain automorphism ofℂ m × Y . © 2018 Wiley Periodicals, Inc.
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