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On rotationally symmetric Kahler-Ricci solitons
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In this paper, the authors constructed rotationally symmetric Kahler-Ricci solitons on the total space of direct sum of fixed hermitian line bundle and its projective compactification.Abstract:
In this note, using Calabi's method, we construct rotationally symmetric Kahler-Ricci solitons on the total space of direct sum of fixed hermitian line bundle and its projective compactification, where the curvature of hermitian line bundle is Kahler-Einstein. These examples generalize the construction of Koiso, Cao and Feldman-Ilmanen-Knopf.read more
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Classification results for expanding and shrinking gradient K\"ahler-Ricci solitons
TL;DR: In this article, it was shown that a Kahler cone appears as the tangent cone of a complete expanding gradient Kahler-Ricci soliton with quadratic curvature decay with derivatives if and only if it has a smooth canonical model.
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Kähler-Ricci flow on projective bundles over Kähler-Einstein manifolds
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On a Conjecture of Candelas and de la Ossa
TL;DR: In this paper, it was shown that the metric completion of a canonical Ricci-flat Kahler metric on the nonsingular part of a projective Calabi-Yau variety X with ordinary double point singularities is a compact metric length space homeomorphic to the projective variety X itself.
References
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Journal ArticleDOI
Métriques kählériennes et fibrés holomorphes
TL;DR: Gauthier-Villars as discussed by the authors implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions).
Journal ArticleDOI
Rotationally Symmetric Shrinking and Expanding Gradient Kähler-Ricci Solitons
TL;DR: In this article, the authors constructed new families of Kahler-Ricci solitons on complex line bundles over ℂℙn−1, n ≥ 2, and exhibited a noncompact Ricci flow that shrinks smoothly and self-similarly for t 0.
Journal ArticleDOI
A new holomorphic invariant and uniqueness of Kähler-Ricci solitons
Gang Tian,Xiaohua Zhu +1 more
TL;DR: In this paper, a new holomorphic invariant is defined on a compact Kahler manifold with positive first Chern class and nontrivial holomorphic vector fields, which is an obstruction to the existence of Kahler-Ricci solitons.
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On Rotationally Symmetric Hamilton’s Equation for Kähler–Einstein Metrics
TL;DR: In this article, rotationally symmetric Hamilton's equation for Kahler-Einstein metric is studied and the solution of an equation converges to a Kahler metric if it exists, even on a compact manifold with positive first Chern class.