Geometric structures and special spinor fields

Discussion of correspondences between geometric structures and special spinors in dimensions 6 and 7. Correspondences of Killing spinors with torsion and geometric structures on a hypersurface and its ambient space.

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1. Verfasser: Hoell, Jos
Beteiligte: Agricola, Ilka (Prof. Dr. habil.) (BetreuerIn (Doktorarbeit))
Format: Dissertation
Sprache:Englisch
Veröffentlicht: Philipps-Universität Marburg 2014
Reine und Angewandte Mathematik
Ausgabe:http://dx.doi.org/10.17192/z2014.0413
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publisher Philipps-Universität Marburg
topic Geometrie
spinor
Mathematik
Zusammenhang
geometrische Struktur
geometry
geometric structure
Spinor
spellingShingle Geometrie
spinor
Mathematik
Zusammenhang
geometrische Struktur
geometry
geometric structure
Spinor
Geometric structures and special spinor fields
Korrespondenzen zwischen geometrischen Strukturen und speziellen Spinoren in Dimensionen 6 und 7. Zusammenhänge zwischen Killing-Spinoren mit Torsion sowie geometrischen Strukturen auf Hyperflächen und deren umgebenden Räumen.
Hoell, Jos
title Geometric structures and special spinor fields
title_short Geometric structures and special spinor fields
title_full Geometric structures and special spinor fields
title_fullStr Geometric structures and special spinor fields
title_full_unstemmed Geometric structures and special spinor fields
title_sort Geometric structures and special spinor fields
contents Korrespondenzen zwischen geometrischen Strukturen und speziellen Spinoren in Dimensionen 6 und 7. Zusammenhänge zwischen Killing-Spinoren mit Torsion sowie geometrischen Strukturen auf Hyperflächen und deren umgebenden Räumen.
ref_str_mv references
description Discussion of correspondences between geometric structures and special spinors in dimensions 6 and 7. Correspondences of Killing spinors with torsion and geometric structures on a hypersurface and its ambient space.
first_indexed 2014-10-29T00:00:00Z
building Fachbereich Mathematik und Informatik
title_alt Geometrische Strukturen und spezielle Spinorfelder
author2 Agricola, Ilka (Prof. Dr. habil.)
author2_role ths
author Hoell, Jos
url http://archiv.ub.uni-marburg.de/diss/z2014/0413/pdf/djh.pdf
oai_set_str_mv ddc:510
open_access
doc-type:doctoralThesis
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dewey-raw 510
dewey-search 510
genre Mathematics
genre_facet Mathematics
topic_facet Mathematik
publishDate 2014
era_facet 2014
last_indexed 2014-10-29T23:59:59Z
institution Reine und Angewandte Mathematik
language English
doi_str_mv http://dx.doi.org/10.17192/z2014.0413
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license_str http://archiv.ub.uni-marburg.de/adm/urhg.html
format Dissertation
thumbnail http://archiv.ub.uni-marburg.de/diss/z2014/0413/cover.png
spelling diss/z2014/0413 Geometric structures and special spinor fields Geometric structures and special spinor fields Korrespondenzen zwischen geometrischen Strukturen und speziellen Spinoren in Dimensionen 6 und 7. Zusammenhänge zwischen Killing-Spinoren mit Torsion sowie geometrischen Strukturen auf Hyperflächen und deren umgebenden Räumen. C. Puhle, Spin(7)-manifolds with parallel torsion form, Commun. Math. Phys. 291, 303-320 (2009). 2009 Spin(7)-manifolds with parallel torsion form C. Puhle, Almost contact metric 5-manifolds and connections with torsion, Differ. Geom. Appl. 30, 85-106 (2012). 2012 Almost contact metric 5-manifolds and connections with torsion T. Houri, H. Takeuchi, Y. Yasui, A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions, Class. Quantum Grav. 30 (2013). 2013 A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions [AFH13] I. Agricola, T. Friedrich, J.Höll, Sp(3) structures on 14-dimensional manifolds, J. Geom. Phys. 69, 12-30 (2013). 2013 Sp(3) structures on 14-dimensional manifolds T. Friedrich, On the spinor representation of surfaces in Euclidean 3-space, J. Geom. Phys. 28, 143-157 (1998). 1998 On the spinor representation of surfaces in Euclidean 3-space [CCD03] G.L. Cardoso, G. Curio, G. Dall'Agata, D. Lüst, D, P. Manousselis, G. Zoupanos, Non- Kähler string backgrounds and their five torsion classes, Nucl. Phys. B 652, 5-34 (2003). 2003 Non- Kähler string backgrounds and their five torsion classes T. Friedrich, S. Ivanov, Parallel spinors and connections with skew-symmetric torsion in string theory, Asian J. Math. 6, 303–335 (2002). 2002 Parallel spinors and connections with skew-symmetric torsion in string theory T. Friedrich, S. Ivanov, Almost contact manifolds, connections with torsion, and par- allel spinors, J. Reine Angew. Math. 559, 217-236 (2003). 2003 Almost contact manifolds, connections with torsion, and parallel spinors [BGM05] C. Bär, P. Gauduchon, A. Moroianu, Generalized Cylinders in Semi-Riemannian and Spin Geometry, Math. Z. 249, 545-580 (2005). 2005 Generalized Cylinders in Semi-Riemannian and Spin Geometry I. Agricola, T. Friedrich, On the holonomy of connections with skew-symmetric torsion, Math. Ann. 328, 711-748 (2004). 2004 On the holonomy of connections with skew-symmetric torsion [AFS05] B. Alexandrov, T. Friedrich, N. Schoemann, Almost Hermitian 6-manifolds revisited, J. Geom. Phys. 53, 1-30 (2005). 2005 Almost Hermitian 6-manifolds revisited D. Conti, S.M. Salamon, Generalized Killing spinors in dimension 5, Trans. Am. Math. Soc. 359 (2007). 2007 Generalized Killing spinors in dimension 5 I. Agricola, T. Friedrich, Geometric structures of vectorial type, J. Geom. Phys. 56, 2403-2414 (2006). 2006 Geometric structures of vectorial type I. Agricola, T. Friedrich, Eigenvalue estimates for Dirac operators with parallel char- acteristic torsion, Diff. Geom. Appl. 26, 613-624 (2008). 2008 Eigenvalue estimates for Dirac operators with parallel characteristic torsion [Sc06] N. Schoemann, Almost hermitian structures with parallel torsion, Dissertation Humbolt-Universität Berlin (2006). 2006 Almost hermitian structures with parallel torsion T.Friedrich, E.C.Kim, The Einstein-Dirac equation on Riemannian spin manifolds, J. The Einstein-Dirac equation on Riemannian spin manifolds T. Friedrich, Dirac Operators in Riemannian Geometry, Graduate Studies in Mathe- matics V. 25, AMS (2000). 2000 Dirac Operators in Riemannian Geometry T.Friedrich, E.C.Kim, Some remarks on the Hijazi inequality and generalizations of the Killing equation for spinors, J. Geom. Phys. 37, 1-14 (2001). 2001 Some remarks on the Hijazi inequality and generalizations of the Killing equation for spinors [Iv04] S. Ivanov, Connections with torsion, parallel spinors and geometry of Spin(7) mani- folds, Math. Res. Lett. 11, 171-186 (2004). 2004 Connections with torsion, parallel spinors and geometry of Spin(7) manifolds [CS02] S.G. Chiossi, S.M. Salamon, The intrinsic torsion of SU(3) and G2 structures, Pro- ceedings of the international conference held in honour of the 60th birthday of A. M. The intrinsic torsion of SU(3) and G2 structures T. Friedrich, Der erste Eigenwert des Dirac-Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung, Math. Nachr. 97, 117-146 (1980). 1980 Der erste Eigenwert des Dirac-Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung T. Friedrich, R. Grunewald, On the first eigenvalue of the Dirac operator on 6- dimensional manifolds, Ann. Glob. Anal. Geom. 3, 265-273 (1985). 1985 On the first eigenvalue of the Dirac operator on 6- dimensional manifolds R. Grunewald, Six-dimensional Riemannian manifolds with a real Killing spinor, Ann. Glob. Anal. Geom. 8, 43-59 (1990). 1990 Six-dimensional Riemannian manifolds with a real Killing spinor O. Kovalski, L. Vanhecke, Classification of five dimensional naturally reductive spaces, Math. Proc. Cambridge Philos. Soc. 97, 445-463 (1985). 1985 Classification of five dimensional naturally reductive spaces J. Simons, On the transitivity of holonomy systems, Ann. of Math. 76 (1962), 213-234. [St09] 1962 On the transitivity of holonomy systems M. Fernández, S. Ivanov, V.Muñoz, L.Ugarte, Nearly hypo structures and compact nearly Kähler 6-manifolds with conical singularities, J. Lond. Math. Soc., II. Ser. 78, 580–604 (2008). 2008 Nearly hypo structures and compact nearly Kähler 6-manifolds with conical singularities M. Fernández, A Classification of Riemannian Manifolds with Structure Group Spin(7), Ann. Mat. Pura Appl., IV. Ser. 143, 101-122 (1986). 1986 A Classification of Riemannian Manifolds with Structure Group Spin(7) [C06] F. Martín Cabrera, SU(3)-structures on hypersurfaces of manifolds with G 2 -structure, Monatsh. Math. 148, 29-50 (2006). 2006 SU(3)-structures on hypersurfaces of manifolds with G 2 -structure [AGI98] V. Apostolov, G. Grantcharov and S. Ivanov, Hermitian structures on twistor spaces, Ann. Glob. Anal. Geom. 16, 291-308 (1998). 1998 Hermitian structures on twistor spaces J. M. Bismut, A local index theorem for non-Kählerian manifolds, Math. Ann. 284, 681-699 (1989). 1989 A local index theorem for non-Kählerian manifolds [Ca09] B. Cappelletti, 3-structures with torsion, Differ. Geom. Appl., 27, 496-506 (2009). 2009 Cappelletti, 3-structures with torsion O. Hijazi, Caractérisation de la sphère par lespremì eres valeurs propres de l'opérateur de Dirac en dimension 3, 4, 7 et 8, C. R. Acad. Sci., Paris, Sér. I 303, 417-419 (1986). 1986 Caractérisation de la sphère par lespremì eres valeurs propres de l'opérateur de Dirac en dimension 3 D. Chinea, J. C. Marrero, Classification of almost contact metric structures, Rev. Roum. Math. Pures Appl. 37, 199-211 (1992). 1992 Classification of almost contact metric structures I. Agricola, J. Höll, Cones of G manifolds and Killing spinors with skew torsion, to appear Ann. Mat. Pura Appl., DOI 10.1007/s10231-013-0393-z. Cones of G manifolds and Killing spinors with skew torsion, to appear Ann Th. Friedrich, G 2 -manifolds with parallel characteristic torsion, Differ. Geom. Appl.25, 632-648 (2007). 2007 G 2 -manifolds with parallel characteristic torsion M. Atiyah, I. Singer, Harmonic spinors and elliptic operators, Arbeitstagung Lecture, Talk of M. Atiyah (1962). 1962 Harmonic spinors and elliptic operators, Arbeitstagung Lecture, Talk of M J. A. Oubiña, New classes of almost contact metric structures, Publ. Math. 32, 187-193 (1985). 1985 New classes of almost contact metric structures R. Cleyton, S. Ivanov, On the geometry of closed G 2 -structures, Commun. Math. Phys. 270, 53-67 (2007). 2007 On the geometry of closed G 2 -structures M. Y. Wang, Parallel Spinors and Parallel Forms, Ann. Global Anal. Geom. 7, 59-68 (1989). 1989 Parallel Spinors and Parallel Forms [Sa89] S.M. Salamon, Riemannian Geometry and holonomy groups, Pitman Res. Notices in Math. Series 201, Harlow: Longman Sci. and Technical (1989). 1989 Riemannian Geometry and holonomy groups M. Fernández, A. Gray, Riemannian manifolds with structure group G 2 , Ann. Mat. Riemannian manifolds with structure group G 2 Naveira, Valencia, Spain, July 8-14, 2001. Singapore: World Scientific. 115-133 (2002). 2001 Singapore: World Scientific M. Okumura, Some remarks on space with a certain contact structure, Tôhoku Math. J. 14, 135-145 (1962). BIBLIOGRAPHY [Ou85] 1962 Some remarks on space with a certain contact structure, Tôhoku Math P. Ivanov, S. Ivanov, SU(3)-instantons and G 2 , Spin(7)-heterotic string solutions, Commun. Math. Phys. 259, No. 1, 79-102 (2005). 2005 Spin(7)-heterotic string solutions M. Berger, Sur les groupes d'holonomie des variétésvariétésà connexion affine et des variétés riemanniennes, Bull. Soc. Math France 83, 279-330 (1955). BIBLIOGRAPHY [Bi89] 1955 Sur les groupes d'holonomie des variétésvariétésà connexion affine et des variétés riemanniennes [Ca25] ´ E. Cartan, Sur les variétésvariétésà connexion affine et la théorie de la relativité généralisée deuxì eme partie), Ann. Ec. Norm. Sup. 42 (1925), 17-88, part two. English transl. of both parts by A. Magnon and A. Ashtekar, On manifolds with an affine connection and the theory of general relativity. Napoli: Bibliopolis (1986). 1925 Sur les variétésvariétésà connexion affine et la théorie de la relativité généralisée deuxì eme partie), Ann. Ec. Norm. Sup 17-88, part two. English transl. of both parts by A. Magnon and A. Ashtekar, On manifolds with an affine connection and the theory of general relativity I. Agricola, The Srní lectures of non-integrable geometries with torsion, Arch. Math. 42 (5), 5-84 (2006). 2006 The Srní lectures of non-integrable geometries with torsion [Ta68] S. Tanno, The topology of contact Riemannian manifolds, Illinois Journ. Math. 12, 700-717 (1968). 1968 The topology of contact Riemannian manifolds, Illinois Journ M. Fernández, A. Fino, L. Ugarte, R. Villacampa, Strong Kähler with torsion struc- tures from almost cantact manifolds, Pac. J. Math. 249, 49-75 (2011). 2011 Strong Kähler with torsion structures from almost cantact manifolds, Pac D. Conti, S.M. Salamon, Reduced holonomy, hypersurfaces and extensions, Int. J. Geom. Methods Mod. Phys. 3, 899-912 (2006). 2006 Reduced holonomy, hypersurfaces and extensions Th. Friedrich, I. Kath, 7-dimensional compact Riemannian manifolds with Killing spinors, Commun. Math. Phys. 133, 543-561 (1990). 1990 7-dimensional compact Riemannian manifolds with Killing spinors C. Bär, Real Killing spinors and holonomy, Comm. Math. Phys. 154 (3), 509-521 (1993). 1993 Real Killing spinors and holonomy Th. Friedrich, I. Kath, Einstein manifolds of dimension five with small first eigenvalue of the Dirac operator, J. Diff. Geom. 29, 263-279 (1989). 1989 Einstein manifolds of dimension five with small first eigenvalue of the Dirac operator [Di28a] P. A. M. Dirac, The Quantum Theory of the Electron I., Proceedings Royal Soc. London (A) 117, 610-624 (1928). 1928 The Quantum Theory of the Electron I [Br87] R. L. Bryant, Metrics with exceptional holonomy, Ann Math. 126, 525-576 (1987). 1987 Metrics with exceptional holonomy S. Stock, Lifting SU(3)-structures to nearly parallel G 2 structures, J. Geom. Phys. 59, 1-7 (2009). 2009 Lifting SU(3)-structures to nearly parallel G 2 structures I. Agricola, T. Friedrich, 3-Sasakian manifolds in dimension seven, their spinors and G 2 -structures, J. Geom. Phys. 60, 326–332 (2010). 2010 3-Sasakian manifolds in dimension seven, their spinors and G 2 -structures A. Gray, L.M. Hervella, The Sixteen Classes of Almost Hermition Manifolds and Their Linear Invariants, Ann. Mat. Pura Appl., IV. Ser. 123, 35–58 (1980). 1980 The Sixteen Classes of Almost Hermition Manifolds and Their Linear Invariants D. Chinea, C. Gonzalez, A Classification of Almost Contact Metric Manifolds, Ann. Mat. Pura Appl., IV. Ser. 156, 15-36 (1990). 1990 A Classification of Almost Contact Metric Manifolds 2014-10-17 Discussion of correspondences between geometric structures and special spinors in dimensions 6 and 7. Correspondences of Killing spinors with torsion and geometric structures on a hypersurface and its ambient space. 2014-10-29 Geometrische Strukturen und spezielle Spinorfelder 2014 opus:5754 2014-10-29 http://dx.doi.org/10.17192/z2014.0413 urn:nbn:de:hebis:04-z2014-04138 Philipps-Universität Marburg ths Prof. Dr. habil. Agricola Ilka Agricola, Ilka (Prof. Dr. habil.) Hoell, Jos Hoell Jos
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