The torsion of spinor connections and related structures.
Klinker, Frank (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Klinker, Frank (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Wlodzimierz M. Mikulski (2006)
Extracta Mathematicae
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Let A be a Weil algebra and V be an A-module with dim V < ∞. Let E → M be a vector bundle and let TE → TM be the vector bundle corresponding to (A,V). We construct canonically a linear semibasic tangent valued p-form Tφ : T E → ΛT*TM ⊗ TTE on TE → TM from a linear semibasic tangent valued p-form φ : E → ΛT*M ⊗ TE on E → M. For the Frolicher-Nijenhuis bracket we prove that [[Tφ, Tψ]] = T ([[φ,ψ]]) for any linear semibasic tangent valued p- and q-forms φ and ψ on E → M. We apply...
Thomas Friedrich (2013)
Communications in Mathematics
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Any 7-dimensional cocalibrated -manifold admits a unique connection with skew symmetric torsion (see [8]). We study these manifolds under the additional condition that the -Ricci tensor vanish. In particular we describe their geometry in case of a maximal number of -parallel vector fields.
Josef Janyška, Martin Markl (2012)
Archivum Mathematicum
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This paper is a continuation of [2], dealing with a general, not-necessarily torsion-free, connection. It characterizes all possible systems of generators for vector-field valued operators that depend naturally on a set of vector fields and a linear connection, describes the size of the space of such operators and proves the existence of an ‘ideal’ basis consisting of operators with given leading terms which satisfy the (generalized) Bianchi–Ricci identities without corrections. ...
Ivan Kolář, Antonella Cabras (2006)
Commentationes Mathematicae Universitatis Carolinae
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We describe the fundamental properties of the infinitesimal actions related with functorial prolongations of principal and associated bundles with respect to fiber product preserving bundle functors. Our approach is essentially based on the Weil algebra technique and an original concept of weak principal bundle.
Waldorf, Konrad (2007)
Theory and Applications of Categories [electronic only]
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