Non-existence of orthogonal coordinates on the complex and quaternionic projective spaces

JOURNAL OF GEOMETRY AND PHYSICS

卷:155

Article

Gauduchon, Paul¹  Moroianu, Andrei² 

[1] Ecole Polytech, CMLS CNRS, Inst Polytech Paris, F-91128 Palaiseau, France

[2] Univ Paris Saclay, CNRS, Lab Math Orsay, F-91405 Orsay, France

关键词: Orthogonal coordinates;    Separation of variables;    Hamilton-Jacobi equation;    Symmetric spaces;   

DOI  :  10.1016/j.geomphys.2020.103770

来源: Elsevier

【 摘 要 】

DeTurck and Yang have shown that in the neighborhood of every point of a 3-dimensional Riemannian manifold, there exists a system of orthogonal coordinates (that is, with respect to which the metric has diagonal form). We show that this property does not generalize to higher dimensions. In particular, the complex projective spaces CPm and the quaternionic projective spaces HPq, endowed with their canonical metrics, do not have local systems of orthogonal coordinates for m, q >= 2. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free