3차원 접촉 다양체에 대한 양적 긴밀성: 부리만 기하학적 접근
본 논문에서는 부리만 기하학적 도구, 특히 접촉 야코비 곡선을 사용하여 3차원 접촉 다양체에서 리브 궤도 주변의 최대 긴밀 근방에 대한 양적 추정을 제시합니다.
Quantitative Tightness of Three-Dimensional Contact Manifolds: A Sub-Riemannian Geometry Approach
This research paper leverages sub-Riemannian geometry to establish quantitative estimates for the maximal tight neighborhood of Reeb orbits in three-dimensional contact manifolds, introducing the concept of contact Jacobi curves to detect overtwisted disks and providing sharp tightness radius estimates based on Schwarzian derivative and canonical curvature bounds.
The Existence of Constant Torsion Knots in Every Isotopy Class
Curves and knots with constant torsion, a property found in elastic rods, can be constructed within every isotopy class using convex integration techniques.
특수 부리만 다양체에서 무한소 등거리 사상의 존재와 연장에 대하여
특수 부리만 다양체에서 주어진 점 주변에 무한소 등거리 사상을 구축하고 이를 더 큰 영역으로 연장할 수 있는 조건을 찾는 것이 이 논문의 목적이다.
特殊部分リーマン多様体上の無限小等距離写像の存在と延長に関する研究
特殊部分リーマン多様体上の無限小等距離写像の局所的な構成と、それらの大域的な延長に関する条件を明らかにする。
アフィン共形キリング ベクトル場と準リッチ ソリトンに関する研究
リーマン多様体上のアフィン共形キリング ベクトル場の性質を明らかにし、そのようなベクトル場を持つ準リッチ ソリトンの性質を解明する。
Three-Dimensional Riemannian Manifolds Associated with Locally Conformal Riemannian Product Manifolds
A 3-dimensional Riemannian manifold (M, g, Q) with a tensor structure Q whose fourth power is the identity is associated with a Riemannian almost product manifold (M, g, P), where P = Q^2. The almost product manifold (M, g, P) is shown to belong to the class of locally conformal Riemannian product manifolds.
エインシュタイン時空における null 超曲面のキャロル幾何学的構造
エインシュタイン時空における shear-free null 超曲面は、固有のコフレーム基底と接続を持つ null 超曲面構造として特徴付けられる。これらの null 超曲面は、キャロル幾何学的構造を持つ。
Reconstructing Planar Curves from Euclidean and Affine Curvatures
Practical algorithms for reconstructing planar curves from their Euclidean or affine curvatures, and estimates on the closeness of reconstructed curves with close curvatures.
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