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101.
We prove that an isometric immersion of a simply connected Riemannian surface in four-dimensional Minkowski space, with given normal bundle and given mean curvature vector , is equivalent to a normalized spinor field solution of a Dirac equation on the surface. Using the immersion of the Minkowski space into the complex quaternions, we also obtain a representation of the immersion in terms of the spinor field. We then use these results to describe the flat spacelike surfaces with flat normal bundle and regular Gauss map in four-dimensional Minkowski space, and also the flat surfaces in three-dimensional hyperbolic space, giving spinorial proofs of results by J.A. Gálvez, A. Martínez and F. Milán. 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(1):423-437
Quaternions, introduced by Hamilton in 1843 as a generalization of complex numbers, have found, in more recent years, a wealth of applications in a number of different areas that motivated the design of efficient methods for numerically approximating the zeros of quaternionic polynomials. In fact, one can find in the literature recent contributions to this subject based on the use of complex techniques, but numerical methods relying on quaternion arithmetic remain scarce. In this paper, we propose a Weierstrass‐like method for finding simultaneously all the zeros of unilateral quaternionic polynomials. The convergence analysis and several numerical examples illustrating the performance of the method are also presented. 相似文献
108.
Mikhail G. Katz Sté phane Sabourau 《Proceedings of the American Mathematical Society》2006,134(4):1189-1195
We prove that C. Loewner's inequality for the torus is satisfied by conformal metrics on hyperelliptic surfaces as well. In genus 2, we first construct the Loewner loops on the (mildly singular) companion tori, locally isometric to away from Weierstrass points. The loops are then transplanted to , and surgered to obtain a Loewner loop on . In higher genus, we exploit M. Gromov's area estimates for -regular metrics on .
109.
Martine Girard. 《Mathematics of Computation》2006,75(255):1561-1583
The group generated by the Weierstrass points of a smooth curve in its Jacobian is an intrinsic invariant of the curve. We determine this group for all smooth quartics with eight hyperflexes or more. Since Weierstrass points are closely related to moduli spaces of curves, as an application, we get bounds on both the rank and the torsion part of this group for a generic quartic having a fixed number of hyperflexes in the moduli space of curves of genus 3.
110.
QiaoLingXIA YiBingSHEN 《数学学报(英文版)》2004,20(6):1029-1046
In this paper, we reformulate the Euler-Lagrange equations of Willmore surfaces in S^n as the flatness of a family of certain loop algebra-valued 1-forms. Therefore we can give the Weierstrass type representation of conformal Willmore surfaces. We also discuss the relations between conformal Willmore surfaces in S^n and minimal surfaces in constant curvature spaces S^n, R^n, H^n, and prove that some special Willmore surfaces can be derived from minimal surfaces in S^n, R^n, H^n. 相似文献