Two-jets of conformal fields along their zero sets

• Autorzy: Andrzej Derdzinski
• Języki publikacji: EN

Abstrakty

EN

The connected components of the zero set of any conformal vector field v, in a pseudo-Riemannian manifold (M, g) of arbitrary signature, are of two types, which may be called ‘essential’ and ‘nonessential’. The former consist of points at which v is essential, that is, cannot be turned into a Killing field by a local conformal change of the metric. In a component of the latter type, points at which v is nonessential form a relatively-open dense subset that is at the same time a totally umbilical submanifold of (M, g). An essential component is always a null totally geodesic submanifold of (M, g), and so is the set of those points in a nonessential component at which v is essential (unless this set, consisting precisely of all the singular points of the component, is empty). Both kinds of null totally geodesic submanifolds arising here carry a 1-form, defined up to multiplications by functions without zeros, which satisfies a projective version of the Killing equation. The conformal-equivalence type of the 2-jet of v is locally constant along the nonessential submanifold of a nonessential component, and along an essential component on which the distinguished 1-form is nonzero. The characteristic polynomial of the 1-jet of v is always locally constant along the zero set.

Słowa kluczowe

EN

Conformal vector field; Fixed-point set; Two-jet

Kategorie tematyczne

• 53B30: Lorentz metrics, indefinite metrics

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 5
• Strony: 1698-1709

Daty

wydano

2012-10-01

online

2012-07-24

Twórcy

autor

Andrzej Derdzinski

• The Ohio State University

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0049-z