We define the notion of evolutes of curves in a hyperbolic plane and establish the relation-ships between singularities of these subjects and geometric invariants of curves under the action of theLorentz group.We also...We define the notion of evolutes of curves in a hyperbolic plane and establish the relation-ships between singularities of these subjects and geometric invariants of curves under the action of theLorentz group.We also describe how we can draw the picture of an evolute of a hyperbolic plane curvein the Poincaré disk.展开更多
借助高等数学知识和几何画板,探索了椭圆内切圆和曲率圆的方程与图象及其之间的关系.研究结果表明:在椭圆的凹侧且与椭圆相切于点P(x0,y0)的最大圆是椭圆在该点的曲率圆;椭圆Γ在点P(acost,bsint)的最大内切圆和曲率圆的方程分别为(x-ca...借助高等数学知识和几何画板,探索了椭圆内切圆和曲率圆的方程与图象及其之间的关系.研究结果表明:在椭圆的凹侧且与椭圆相切于点P(x0,y0)的最大圆是椭圆在该点的曲率圆;椭圆Γ在点P(acost,bsint)的最大内切圆和曲率圆的方程分别为(x-ca2cost)2+y2=ba22(b2+c2sin2t)和(x-ca2cos3t)2+(y+cb2sin3t)2=a21b2(b2+c2sin2t)3;椭圆Γ的内切圆者的圆心轨迹为线段:y=0且-ca2 x ca2,曲率圆的圆心轨迹为(c2x/a23)23+(c2y/2b3)23=1.展开更多
In this paper,we study the pseudo-spherical evolutes of curves in three dimensional hyperbolic space.We use techniques from singularity theory to investigate the singularities of pseudo-spherical evolutes and establis...In this paper,we study the pseudo-spherical evolutes of curves in three dimensional hyperbolic space.We use techniques from singularity theory to investigate the singularities of pseudo-spherical evolutes and establish some relationships between singularities of these curves and geometric invariants of curves under the action of the Lorentz group.Besides,we defray with illustration some computational examples in support our main results.展开更多
文摘We define the notion of evolutes of curves in a hyperbolic plane and establish the relation-ships between singularities of these subjects and geometric invariants of curves under the action of theLorentz group.We also describe how we can draw the picture of an evolute of a hyperbolic plane curvein the Poincaré disk.
文摘借助高等数学知识和几何画板,探索了椭圆内切圆和曲率圆的方程与图象及其之间的关系.研究结果表明:在椭圆的凹侧且与椭圆相切于点P(x0,y0)的最大圆是椭圆在该点的曲率圆;椭圆Γ在点P(acost,bsint)的最大内切圆和曲率圆的方程分别为(x-ca2cost)2+y2=ba22(b2+c2sin2t)和(x-ca2cos3t)2+(y+cb2sin3t)2=a21b2(b2+c2sin2t)3;椭圆Γ的内切圆者的圆心轨迹为线段:y=0且-ca2 x ca2,曲率圆的圆心轨迹为(c2x/a23)23+(c2y/2b3)23=1.
基金Supported by Natural Science Foundation of Anhui Province(No.1908085MA05)University Natural Science Research Project of Anhui Province(No.KJ2019A0590)Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province(No.gxyqZD2020022).
文摘In this paper,we study the pseudo-spherical evolutes of curves in three dimensional hyperbolic space.We use techniques from singularity theory to investigate the singularities of pseudo-spherical evolutes and establish some relationships between singularities of these curves and geometric invariants of curves under the action of the Lorentz group.Besides,we defray with illustration some computational examples in support our main results.
