标题： 位错四极子的几何和拓扑方面：共形度量和自力 显示英文标题

标题： Geometric and Topological Aspects of Quadrupoles of Disclinations: Conformal Metrics and Self-Forces

摘要： 我们研究了在$(2+1)$维度下使用共形度量方法的焦散四极配置的几何和物理效应。 考虑了两种情况：一种是线性四极子，它通过一个$\cos(2\theta)$作为轮廓诱导各向异性曲率；另一种是方形四极子，它产生更高角谐波的更各向同性的场。 我们解出了共形因子的泊松方程，并计算了相应的格林函数。 利用这些构型，我们评估了线性源的静电和磁静自能以及自力。 结果揭示了对称性和曲率如何影响自相互作用效应，与静电情况相比，磁静自力表现出符号反转。 讨论了与先前位错和宇宙弦模型的联系，潜在应用包括石墨烯、向列相和引力类比。 显示英文摘要

摘要： We study the geometric and physical effects of quadrupolar configurations of disclinations using a conformal metric approach in $(2+1)$ dimensions. Two cases are considered: a linear quadrupole, inducing anisotropic curvature with a $\cos(2\theta)$ as profile, and a square quadrupole, yielding a more isotropic field with higher angular harmonics. We solve the Poisson equation for the conformal factor and compute the corresponding Green functions. Using these configurations, we evaluated the electrostatic and magnetostatic self-energies and self-forces for linear sources. The results reveal how symmetry and curvature influence self-interaction effects, with the magnetostatic self-force exhibiting a sign reversal compared to the electrostatic case. Connections with previous models of dislocations and cosmic strings are discussed, with potential applications in graphene, nematics, and gravitational analogs.