caa a22 4500 605496269 CHVBK 20210128100535.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10231-013-0393-z doi (NATIONALLICENCE)springer-10.1007/s10231-013-0393-z Cones of $$G$$ G manifolds and Killing spinors with skew torsion [Elektronische Daten] [Ilka Agricola, Jos Höll] This paper is devoted to the systematic investigation of the cone construction for Riemannian $$G$$ G manifolds $$M$$ M , endowed with an invariant metric connection with skew torsion $$\nabla ^c$$ ∇ c , a ‘characteristic connection.' We show how to define a $$\bar{G}$$ G ¯ structure on the cone $$\bar{M}=M\times \mathbb {R}^+$$ M ¯ = M × R + with a cone metric, and we prove that a Killing spinor with torsion on $$M$$ M induces a spinor on $$\bar{M}$$ M ¯ that is parallel for the characteristic connection of the $$\bar{G}$$ G ¯ structure. We establish the explicit correspondence between classes of metric almost contact structures on $$M$$ M and almost Hermitian classes on $$\bar{M}$$ M ¯ , respectively, between classes of $$G_2$$ G 2 structures on $$M$$ M and $$\mathrm {Spin}(7)$$ Spin ( 7 ) structures on $$\bar{M}$$ M ¯ . Examples illustrate how this ‘cone correspondence with torsion' works in practice. Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2013 Cone of Riemannian manifold nationallicence Metric connection with skew torsion nationallicence Characteristic connection nationallicence $$G$$ G Structure nationallicence Killing spinor with torsion nationallicence Parallel spinor nationallicence $$G_2$$ G 2 manifold nationallicence $$\mathrm {Spin}(7)$$ Spin ( 7 ) manifold nationallicence almost contact metric manifold nationallicence $$\alpha $$ α -Sasakian manifold nationallicence almost Hermitian manifold nationallicence Hyper-Kähler manifold with torsion nationallicence Tanno deformation nationallicence Agricola Ilka Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Strasse, 35032, Marburg, Germany aut Höll Jos Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Strasse, 35032, Marburg, Germany aut Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/3(2015-06-01), 673-718 0373-3114 194:3<673 2015 194 10231 https://doi.org/10.1007/s10231-013-0393-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-013-0393-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Agricola Ilka Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Strasse, 35032, Marburg, Germany aut NATIONALLICENCE 700 1- Höll Jos Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Strasse, 35032, Marburg, Germany aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/3(2015-06-01), 673-718 0373-3114 194:3<673 2015 194 10231