ﻻ يوجد ملخص باللغة العربية
In a joint work with N. Mok in 1997, we proved that for an irreducible representation $G subset {bf GL}(V),$ if a holomorphic $G$-structure exists on a uniruled projective manifold, then the Lie algebra of $G$ has nonzero prolongation. We tried to generalize this to an arbitrary connected algebraic subgroup $G subset {bf GL}(V)$ and a complex manifold containing an immersed rational curve, but the proposed proof had a flaw.
We provide an algorithm to check whether two rational space curves are related by a similarity. The algorithm exploits the relationship between the curvatures and torsions of two similar curves, which is formulated in a computer algebra setting. Heli
In this paper, we study unirational differential curves and the corresponding differential rational parametrizations. We first investigate basic properties of proper differential rational parametrizations for unirational differential curves. Then we
We study unbendable rational curves, i.e., nonsingular rational curves in a complex manifold of dimension $n$ with normal bundles isomorphic to $mathcal{O}_{mathbb{P}^1}(1)^{oplus p} oplus mathcal{O}_{mathbb{P}^1}^{oplus (n-1-p)}$ for some nonnegativ
Consider a simple algebraic group G of adjoint type, and its wonderful compactification X. We show that X admits a unique family of minimal rational curves, and we explicitly describe the subfamily consisting of curves through a general point. As an
We study a cone structure ${mathcal C} subset {mathbb P} D$ on a holomorphic contact manifold $(M, D subset T_M)$ such that each fiber ${mathcal C}_x subset {mathbb P} D_x$ is isomorphic to a Legendrian submanifold of fixed isomorphism type. By chara