PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2012 | 10 | 5 | 1698-1709
Tytuł artykułu

Two-jets of conformal fields along their zero sets

Treść / Zawartość
Warianty tytułu
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
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
5
Strony
1698-1709
Opis fizyczny
Daty
wydano
2012-10-01
online
2012-07-24
Twórcy
Bibliografia
  • [1] Beig R., Conformal Killing vectors near a fixed point, Institut für Theoretische Physik, Universität Wien, 1992 (unpublished manuscript)
  • [2] Belgun F., Moroianu A., Ornea L., Essential points of conformal vector fields, J. Geom. Phys., 2011, 61(3), 589–593 http://dx.doi.org/10.1016/j.geomphys.2010.11.007
  • [3] Capocci M.S., Essential conformal vector fields, Classical Quantum Gravity, 1999, 16(3), 927–935 http://dx.doi.org/10.1088/0264-9381/16/3/021
  • [4] Derdzinski A., Zeros of conformal fields in any metric signature, Classical Quantum Gravity, 2011, 28(7), #075011 http://dx.doi.org/10.1088/0264-9381/28/7/075011
  • [5] Derdzinski A., Maschler G., A moduli curve for compact conformally-Einstein Kähler manifolds, Compos. Math., 2005, 141(4), 1029–1080 http://dx.doi.org/10.1112/S0010437X05001612
  • [6] Hall G.S., Symmetries and Curvature Structure in General Relativity, World Sci. Lecture Notes Phys., 46, World Scientific, River Edge, 2004 http://dx.doi.org/10.1142/1729
  • [7] Kobayashi S., Fixed points of isometries, Nagoya Math. J., 1958, 13, 63–68
  • [8] Lampe M., On conformal connections and infinitesimal conformal transformations, PhD thesis, Universität Leipzig, 2010
  • [9] Milnor J., Morse Theory, Ann. of Math. Stud., 51, Princeton University Press, Princeton, 1963
  • [10] Weyl H., Zur Infinitesimalgeometrie: Einordnung der projektiven und der konformen Auffassung, Nachrichten von der Königlichen Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen, 1921, 99–112
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0049-z
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.