Results 1 to 10 of about 51 (44)
Journal of Geometric Analysis, 2022 AbstractWe classify all homogeneous Kobayashi-hyperbolic manifolds of dimension$$n \ge 2$$n≥2whose group of holomorphic automorphisms has dimension either$$n^2 - 7$$n2-7or$$n^2 - 8.$$n2-8.This paper continues the work of A. Isaev, who classified all such manifolds with automorphism group dimension$$n^2 - 6$$n2-6and greater.
Elliot Herrington
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Further Steps Towards Classifying Homogeneous Kobayashi-Hyperbolic Manifolds with High-Dimensional Automorphism Group [PDF]
Journal of Geometric Analysis, 2019 We determine all connected homogeneous Kobayashi-hyperbolic manifolds of dimension $n\ge 4$ whose group of holomorphic automorphisms has dimension either $n^2-4$, or $n^2-5$, or $n^2-6$. This paper continues a series of articles that achieve classifications for automorphism group dimension $n^2-3$ and greater.
Alexander Isaev, Isaev Alexander
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Homogeneous Kobayashi-hyperbolic manifolds with high-dimensional group of holomorphic automorphisms [PDF]
Asian Journal of Mathematics, 2019 We determine all connected homogeneous Kobayashi-hyperbolic manifolds of dimension $n\ge 2$ whose holomorphic automorphism group has dimension $n^2-2$. This result complements an existing classification for automorphism group dimension $n^2-1$ and greater obtained without the homogeneity assumption.
Isaev Alexander
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Kobayashi hyperbolicity in Riemannian manifolds
Journal of Geometric AnalysisWe study the boundary behavior of the Kobayashi-Royden metric and the Kobayashi hyperbolicity of domains in Riemannian manifolds. As an application, we prove a Fatou type theorem on the existence, almost everywhere, of non tangential limits for bounded conformal harmonic immersed discs.
Gaussier Hervé +2 more
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Properties and examples of Kobayashi hyperbolic Riemannian manifolds
Complex Analysis and Its SynergiesWe prove an analogue of the Brody lemma in the framework of Riemannian manifolds. We also present new examples of Riemannian manifolds that are hyperbolic in the sense of Kobayashi.
Gaussier Hervé +2 more
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A note on Lang's conjecture for quotients of bounded domains [PDF]
Épijournal de Géométrie Algébrique, 2021 It was conjectured by Lang that a complex projective manifold is Kobayashi hyperbolic if and only if it is of general type together with all of its subvarieties.
Sébastien Boucksom, Simone Diverio
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ON KOBAYASHI HYPERBOLICITY OF ALMOST COMPLEX MANIFOLDS
Abstract and Applied Analysis, 2004 KHU QUOC ANH, DO DUC THAI
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Kobayashi Non-hyperbolicity of Calabi–Yau Manifolds Via Mirror Symmetry [PDF]
Communications in Mathematical Physics, 2020 8 pages, comments are ...
Ljudmila Kamenova, Cumrun Vafa
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Invariant holomorphic foliations on Kobayashi hyperbolic homogeneous manifolds [PDF]
Proceedings of the American Mathematical Society, 2015 Let $M$ be a Kobayashi hyperbolic homogenous manifold. Let $\mathcal F$ be a holomorphic foliation on $M$ invariant under a transitive group $G$ of biholomorphisms. We prove that the leaves of $\mathcal F$ are the fibers of a holomorphic $G$-equivariant submersion $π\colon M \to N$ onto a $G$-homogeneous complex manifold $N$.
Bracci F., Iannuzzi A., McKay B.
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CONNECTIONS ON ALMOST COMPLEX FINSLER MANIFOLDS AND KOBAYASHI HYPERBOLICITY [PDF]
Journal of the Korean Mathematical Society, 2007 In this paper, we establish a necessary condition in terms of curvature for the Kobayashi hyperbolicity of a class of almost complex Finsler manifolds. For an almost complex Finsler manifold with the condition (R), so-called Rizza manifold, we show that there exists a unique connection compatible with the metric and the almost complex structure which ...
Dae-Yeon Won, Nany Lee
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