báo cáo hóa học:" Research Article First-Order Twistor Lifts ˜ Bruno Ascenso Simoes1, 2"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article First-Order Twistor Lifts ˜ Bruno Ascenso Simoes1, 2 | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 594843 26 pages doi 2010 594843 Research Article First-Order Twistor Lifts Bruno Ascenso Similes1 2 1 Centro de Matematica e Aplicacoes Fundamentais Universidade de Lisboa Av. Prof. Gama Pinto 2 1649-003 Lisbon Portugal 2 Universidade Lusofona Núcleo de Investigacão em Matemdtica Campo Grande 376 1749-024 Lisbon Portugal Correspondence should be addressed to Bruno Ascenso Simoes Received 30 December 2009 Accepted 30 March 2010 Academic Editor Yuming Xing Copyright 2010 Bruno Ascenso Simoes. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. The use of twistor methods in the study of Jacobi fields has proved quite fruitful leading to a series of results. L. Lemaire and J. C. Wood proved several properties of Jacobi fields along harmonic maps from the two-sphere to the complex projective plane and to the three- and four-dimensional spheres by carefully relating the infinitesimal deformations of the harmonic maps to those of the holomorphic data describing them. In order to advance this programme we prove a series of relations between infinitesimal properties of the map and those of its twistor lift. Namely we prove that isotropy and harmonicity to first order of the map correspond to holomorphicity to first order of its lift into the twistor space relatively to the standard almost complex structures J1 and J2. This is done by obtaining first-order analogues of classical twistorial constructions. 1. Introduction Harmonic maps are mappings p between Riemannian manifolds M and N which extremize the energy functional E v 1 iiM 2 M 2 A Wg. Letting TM denote the tangent bundle of M one can locally characterize harmonic maps as solutions of the nonlinear second-order differential equation

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