Properties of manifolds with skew-symmetric torsion and special holonomy

By Anna Fino, G. Grantcharov. 2004

153 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/950bd3e7a98c239eeef74d165fd89616aae048b1

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Citations in the corpus

Hermitian structures on six-dimensional nilmanifolds (2004, unknown): “Keywords: Hermitian structure, Kähler with torsion structure, balanced metric, locally conformal Kähler structure, generalized Hopf metric, nilmanifold MSC 2000: 53C55; 17B30, 32G05”
A survey on strong KT structures (2009, methodology): “and thus there are no left-invariant holomorphic (3, 0)-forms on M. Since the holonomy of the Bismut connection is contained in SU(3), then by [ 16, Theorem 4.1 ] (M, J) cannot admit any non-vanishing holomorphic (3, 0)-form.”
Balanced Hermitian geometry on 6-dimensional nilmanifolds (2011, methodology): “It is proved in [9] that if there is a J-Hermitian metric on M such that the holonomy of the associated Bismut connection is contained in SU(n) then there is an invariant J-Hermitian metric on M which is balanced in the sense of [18].”
Blow-ups and resolutions of strong K\"ahler with torsion metrics (2008, background): “This family was already considered in [14] for Hermitian structures whose Bismut connection has holonomy in SU(3) and it was proved that for any t and s 6= 0 the Lie algebra nt,s is isomorphic to the Lie algebra of the complex Heisenberg group H 3 with structure equations  ”
Non-K\"ahler Calabi-Yau manifolds (2014, background): “much studied in the mathematical physics literature [2, 21, 24, 38, 42, 45, 61], and Conjecture 4.”
Non-Kähler Calabi-Yau manifolds (2014, background): “much studied in the mathematical physics literature [2, 21, 24, 38, 42, 45, 61], and Conjecture 4.”
Generalized Kähler Manifolds, Commuting Complex Structures, and Split Tangent Bundles (2007, background): “Secondly, an example from [9] (combined with a standard averaging argument [6, 12]) shows there are compact complex manifolds whose holomorphic tangent bundle splits and defines two transversal foliations with Kähler leaves but which do not admit any Hermitian metric with ∂∂̄-closed fundamental form”
Balanced Hermitian structures on almost abelian Lie algebras (2020, methodology): “Recall that, by the symmetrization process described in [10, 22, 55], the existence of an SKT (resp.”
Six-Dimensional Solvmanifolds with Holomorphically Trivial Canonical Bundle (2014, methodology): “Notice that the symmetrization process can be applied to this situation to conclude that the existence of SKT, balanced or sG metrics on M reduces to the level of the Lie algebra g of G (see [7, 11] for more details).”
Ricci Curvatures on Hermitian manifolds (2014, background): “cular, the total scalar curvatures are the same (up to a normalization constant 2) if and only if the manifold is Kahler, i.e. T= 0. A similar formulation is also observed by Gauduchon [23]. See also [56, 57, 3, 9, 10, 1, 31, 21, 4, 40, 32] for some special cases. According to the diﬀerent types of ”
A correction to “Tamed symplectic forms and strong Kähler with torsion metrics” (2012, methodology): “We can suppose that g is left-invariant (see [12, 43]).”