اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدReal analytic complete non-compact surfaces in Euclidean space with finite total curvature arising as solutions to ODEs
485
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We use the solution space of a pair of ODEs of at least second order to construct a smooth surface in Euclidean space. We describe when this surface is a proper embedding which is geodesically complete with finite total Gauss curvature. If the associated roots of the ODEs are real and distinct, we give a universal upper bound for the total Gauss curvature of the surface which depends only on the orders of the ODEs and we show that the total Gauss curvature of the surface vanishes if the ODEs are second order. We examine when the surfaces are asymptotically minimal.
قيم البحث
اقرأ أيضاً
We prove that for a solution $(M^n,g(t))$, $tin[0,T)$, where $T<infty$, to the Ricci flow with bounded curvature on a complete non-compact Riemannian manifold with the Ricci curvature tensor uniformly bounded by some constant $C$ on $M^ntimes [0,T)$,
the curvature tensor stays uniformly bounded on $M^ntimes [0,T)$. Some other results are also presented.
In this paper, we completely classify all compact 4-manifolds with positive isotropic curvature. We show that they are diffeomorphic to $mathbb{S}^4,$ or $mathbb{R}mathbb{P}^4$ or quotients of $mathbb{S}^3times mathbb{R}$ by a cocompact fixed point f
ree subgroup of the isometry group of the standard metric of $mathbb{S}^3times mathbb{R}$, or a connected sum of them.
We construct, for the first time, Abelian-Higgs vortices on certain compact surfaces of constant negative curvature. Such surfaces are represented by a tessellation of the hyperbolic plane by regular polygons. The Higgs field is given implicitly in t
erms of Schwarz triangle functions and analytic solutions are available for certain highly symmetric configurations.
For Legendre curves, we consider surfaces of revolution of frontals. The surface of revolution of a frontal can be considered as a framed base surface. We give the curvatures and basic invariants for surfaces of revolution by using the curvatures of
Legendre curves. Moreover, we give properties of surfaces of revolution with singularities and cones.
We characterize singularities of focal surfaces of wave fronts in terms of differential geometric properties of the initial wave fronts. Moreover, we study relationships between geometric properties of focal surfaces and geometric invariants of the initial wave fronts.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
