Local obstructions to projective surfaces admitting skew-symmetric Ricci tensor

JOURNAL OF GEOMETRY AND PHYSICS

卷:76

Article

Randall, Matthew

关键词: Projective differential geometry;    Overdetermined system of PDEs;    Invariant differential operators;   

DOI  :  10.1016/j.geomphys.2013.10.019

来源: Elsevier

【 摘 要 】

The equation determining whether a projective structure admits a connection in its given projective class that has skew-symmetric Ricci tensor is an overdetermined system of semi-linear partial differential equations which we call the projective Einstein-Weyl (pEW) equation. In 2-dimensions, we give local obstructions for projective surfaces to admit such a connection in its projective class. The obstructions are the resultants of polynomial equations that have to be satisfied for there to admit any pEW solution. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free