Calabi-Yau connections with torsion on toric bundles

By D. Grantcharov, G. Grantcharov, Yat Sun Poon. 2003

91 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ed4361339671b2623e21535755aa69970e62e55e

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In Geometry and Topology

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Citations in the corpus

On the existence of balanced and SKT metrics on nilmanifolds (2015, background): “ω is co-closed, i.e. d∗ω = 0, where d∗ denotes the formal adjoint operator of d with respect to the metric g. SKT metrics were introduced by Bismut in [6] and further studied in many papers (see e.g. [13, 14, 11, 20, 18, 19, 22] and the references therein), while balanced metrics were introduced and”
Non-Kähler Calabi-Yau geometry and pluriclosed flow (2021, unknown): “Then, a direct calculation shows that [35] ddω = π∗(∆(eu)ω2 Z − α(2) − ω(2) Z),”
Ricci Curvatures on Hermitian manifolds (2014, background): “For more works on Hermitian manifolds with specials metrics, we refer the reader to [1, 2, 4, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 27, 21, 36, 39, 38, 41, 49, 42, 43, 44] and the references therein.”
Non-K\"ahler Calabi-Yau manifolds (2014, background): “On the other hand, much interest has been devoted to studying non-Kähler compact complex manifolds with holomorphically trivial (or more generally torsion) canonical bundle, and many examples can be found in [6, 15, 17, 20, 23, 33, 35, 36, 37, 40, 43, 53, 60, 78, 83, 86] and references therein.”
A survey on strong KT structures (2009, background): “Very interesting examples of 6-dimensional simply-connected strong KT manifolds were found in [21] by using torus bundles.”
Special Hermitian metrics on compact solvmanifolds (2015, methodology): “SKT metric is given in [14]. Other examples of SKT metrics on compact manifolds are given by the connected sum of products of spheres in view of the following Theorem 3.4 (Grantcharov-Grantcharov-Poon[28]). For any positive integer k ≥ 1, the manifold Mk = (k −1)(S2 ×S4)♯k(S3 ×S3) admits an SKT stru”