Calabi-Yau metrics on canonical bundles of complex flag manifolds
Eder M. Correa, Lino Grama
TL;DR
This paper constructs explicit complete Calabi-Yau metrics on the canonical bundles of complex flag manifolds using Lie theory and the Calabi ansatz, providing new examples of noncompact Ricci-flat Kähler manifolds.
Contribution
It offers an explicit Lie-theoretic description of Calabi-Yau metrics on canonical bundles of generalized flag manifolds, including non-toric examples.
Findings
Explicit Ricci-flat Kähler metrics on canonical bundles of flag manifolds.
New noncompact Calabi-Yau examples including Grassmann and full flag manifolds.
Use of Lie theory and Calabi ansatz for metric construction.
Abstract
In the present paper we provide a description of complete Calabi-Yau metrics on the canonical bundle of generalized complex flag manifolds. By means of Lie theory we give an explicit description of complete Ricci-flat K\"ahler metrics obtained through the Calabi ansatz technique. We use this approach to provide several explicit examples of noncompact complete Calabi-Yau manifolds, these examples include canonical bundles of non-toric flag manifolds (e.g. Grassmann manifolds and full flag manifolds).
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