arXiv subjects
Publications and source records attributed to Ryoichi Kobayashi.
We show that a 1-parameter family Ricci flow ancient solutions arises from the natural collapsings of the twistor space of positive quaternion Kähler manifolds. We use these ancient solutions to show that a positive quaternion Kähler manifold is isometric to one of the Wolf spaces.
We give a metric characterization of the Euclidean sphere in terms of the lower bound of the sectional curvature and the length of the shortest closed geodesics.
The twistor space of self-dual positive Einstein manifolds naturally admits two 1-parameter families of Riemannian metrics, one is the family of canonical deformation metrics and the other is the family introduced by B. Chow and D. Yang in 1989. The purpose of this paper is to compare these two families. In particular we compare the Ricci tensor and the behavior under the Ricci flow of these families. As an application, we propose a new proof to the fact that a locally irreducible self-dual positive Einstein 4-manifold is isometric to either $S^4$ with a standard metric or $\PP^2(\C)$ with a Fubini-Study metric.
We propose an affine version of the Schwarz map for the hypergeometric differential equation, and study its image when the monodromy group is finite.
A new proof of the Second Main Theorem with truncation level 1 for Zariski-dense holomorphic curves into Abelian varieties, which has just been proved by Yamanoi [Y2], is presented. Our proof is based on the idea of the "Radon transform" introduced in [K2] combined with consideration on certain singular perturbation of the probability measures on the parameter space which appears in the "Radon transform".
We give a metric characterization of the Euclidean sphere in terms of the lower bound of the sectional curvature and the length of the shortest closed geodesics.