Results 1 to 10 of about 4,225 (93)

Continuing the Classification of Homogeneous Kobayashi-Hyperbolic Manifolds with High-Dimensional Automorphism Group [PDF]

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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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.
A. Isaev
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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
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Properties and examples of Kobayashi hyperbolic Riemannian manifolds

Complex Analysis and Its Synergies
We 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.
Hervé Gaussier, Alexandre Sukhov
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Kobayashi hyperbolicity in Riemannian manifolds

Journal of Geometric Analysis
We 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.
Hervé Gaussier, Alexandre Sukhov
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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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Homogeneous Kobayashi-hyperbolic manifolds with automorphism group of subcritical dimension [PDF]

Complex Variables and Elliptic Equations, 2017
arXiv admin note: substantial text overlap with arXiv:1709 ...
A. Isaev
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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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The metric compactification of a Kobayashi hyperbolic complex manifold and a Denjoy–Wolff theorem

International Journal of Mathematics
We study the metric compactification of a Kobayashi hyperbolic complex manifold [Formula: see text] equipped with the Kobayashi distance [Formula: see text]. We show that this compactification is genuine[Formula: see text]—[Formula: see text]i.e. [Formula: see text] embeds as a dense open subset[Formula: see text]—[Formula: see text]even without ...
Vikramjeet Singh Chandel, Nishith Mandal
openaire   +3 more sources