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Th. Friedrich (1980). "Der erste
Eigenwert des Dirac Operators einer kompakten, Riemannschen Mannigfaltigkei nichtnegativer SkalarkrĂĽmmung".
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By the more narrow definition, commonly used in mathematics, the term
Killing spinor indicates those
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Th. Friedrich (1989). "On the conformal relation between twistors and
Killing spinors".
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658:(1987). "Spin manifolds, Killing spinors and the universality of Hijazi inequality".
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Another equivalent definition is that
Killing spinors are the solutions to the
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Supplemento dei
Rendiconti del Circolo Matematico di Palermo, Serie II
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is compact, and the spinor field is called a ``real spinor field."
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318:, in particular for finding solutions which preserve some
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322:. They are a special kind of spinor field related to
828:"Twistor and Killing spinors in Lorentzian geometry,"
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is 0, then the spinor field is parallel; finally, if
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155:{\displaystyle \nabla _{X}\psi =\lambda X\cdot \psi }
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Killing and
Twistor Spinors on Lorentzian Manifolds,
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857:(paper by Christoph Bohle) (postscript format)
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301:then the spinor is called a parallel spinor.
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244:{\displaystyle \lambda \in \mathbb {C} }
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801:Dirac Operators in Riemannian Geometry
735:Communications in Mathematical Physics
703:Dirac Operators in Riemannian Geometry
443:{\displaystyle Ric=4(n-1)\alpha ^{2}}
7:
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731:"Real Killing spinors and holonomy"
885:. You can help Knowledge (XXG) by
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16:Type of Dirac operator eigenspinor
14:
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64:for a so-called Killing number.
583:{\displaystyle {\mathcal {M}}}
515:{\displaystyle {\mathcal {M}}}
474:Types of Killing spinor fields
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379:{\displaystyle {\mathcal {M}}}
355:{\displaystyle {\mathcal {M}}}
1:
805:American Mathematical Society
729:Bär, Christian (1993-06-01).
707:American Mathematical Society
968:
864:
799:Friedrich, Thomas (2000),
782:Princeton University Press
701:Friedrich, Thomas (2000),
498:is purely imaginary, then
470:is the Killing constant.
294:{\displaystyle \lambda =0}
251:is a constant, called the
53:. The term is named after
952:Riemannian geometry stubs
610:Mathematische Nachrichten
774:Michelsohn, Marie-Louise
623:10.1002/mana.19800970111
937:Structures on manifolds
559:{\displaystyle \alpha }
539:{\displaystyle \alpha }
491:{\displaystyle \alpha }
463:{\displaystyle \alpha }
221:Clifford multiplication
188:{\displaystyle \nabla }
45:spinors which are also
881:-related article is a
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212:{\displaystyle \cdot }
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324:Killing vector fields
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268:{\displaystyle \psi }
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104:{\displaystyle \psi }
709:, pp. 116–117,
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932:Riemannian geometry
879:Riemannian geometry
772:Lawson, H. Blaine;
672:1987LMaPh..13..331L
524:noncompact manifold
847:Killing's Equation
747:10.1007/BF02102106
680:10.1007/bf00401162
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25:is a term used in
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388:Einstein manifold
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55:Wilhelm Killing
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839:Dirac Operator
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741:(3): 509–521.
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51:Dirac operator
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306:Applications
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90:spinor field
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47:eigenspinors
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19:
18:
666:: 331–334.
617:: 117–146.
27:mathematics
926:Categories
832:Helga Baum
594:References
334:Properties
77:Riemannian
37:Definition
755:1432-0916
688:121971999
554:α
534:α
486:α
458:α
432:α
422:−
283:λ
263:ψ
234:∈
231:λ
207:⋅
183:∇
150:ψ
147:⋅
141:λ
135:ψ
126:∇
99:ψ
776:(1989).
644:: 59–75.
450:, where
175:, where
168:for all
83:manifold
20:Killing
947:Spinors
668:Bibcode
49:of the
43:twistor
31:physics
811:
788:
753:
713:
686:
386:is an
75:on a
22:spinor
877:This
766:Books
684:S2CID
526:; if
522:is a
390:with
275:. If
88:is a
883:stub
809:ISBN
786:ISBN
751:ISSN
711:ISBN
326:and
314:and
223:and
80:spin
33:.
29:and
830:by
743:doi
739:154
676:doi
619:doi
478:If
338:If
255:of
219:is
928::
807:,
803:,
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780:.
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682:.
674:.
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662:.
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613:.
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71:A
57:.
914:e
907:t
900:v
889:.
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745::
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678::
670::
625:.
621::
576:M
508:M
436:2
428:)
425:1
419:n
416:(
413:4
410:=
407:c
404:i
401:R
372:M
348:M
289:0
286:=
238:C
173:X
144:X
138:=
130:X
86:M
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