Geometry of quaternionic Kähler connections with torsion

By Stefan Ivanov. 2000

48 citations recorded by the source corpus.

Abstract The target space of a (4,0) supersymmetric two-dimensional sigma model with Wess–Zumino term has a connection with totally skew-symmetric torsion and holonomy contained in SP( n )·SP(1), QKT connection. We study the geometry of QKT connections. We find conditions to the existence of a QKT connection and prove that if it exists it is unique. We show that QKT geometry persist in a conformal class of metrics which allows us to obtain a lot of (compact) examples of QKT manifolds. We present a (local) description of four-dimensional homogeneous QKT structures relying on the known result of naturally reductive homogeneous Riemannian manifolds. We consider Einstein-like QKT manifold and find closed relations with Einstein–Weyl geometry in dimension 4.

Subfields: Applied Mathematics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/18ea2c04ec2a9d7b48b7c618c799e09db404ab27

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In Applied Mathematics

In Geometry and Topology

In Nuclear and High Energy Physics

Citations in the corpus

Superstrings with intrinsic torsion (2003, background): “almost quaternionic manifolds are given in [ 31 ].) One also notes the relation”
Vanishing theorems and string backgrounds (2000, background): “This leads to the equality of the three Lee forms [28, 36 ], i.e.”
Maximally homogeneous para-CR manifolds of semisimple type (2006, unknown): “Almost quaternionic or almost hyperhermitian structures admitting a structure preserving connection with totally skew-symmetric torsion have been introduced and given various characterisations in [41, 32, 42 , 16].”