scholarly journals The intrinsic torsion of almost quaternion-Hermitian manifolds

2008 ◽  
Vol 58 (5) ◽  
pp. 1455-1497 ◽  
Author(s):  
Francisco Martín Cabrera ◽  
Andrew Swann
Keyword(s):  
Hermitian Manifolds ◽  
Intrinsic Torsion

Harmonic G-structures

2009 ◽  
Vol 146 (2) ◽  
pp. 435-459 ◽  
Author(s):  
J. C. GONZÁLEZ–DÁVILA ◽  
F. MARTÍN CABRERA
Keyword(s):  
Riemannian Manifold ◽  
Critical Points ◽  
Compact Riemannian Manifold ◽  
Harmonic Maps ◽  
Energy Functional ◽  
Second Variation ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Intrinsic Torsion ◽  
First And Second Variation

AbstractFor closed and connected subgroups G of SO(n), we study the energy functional on the space of G-structures of a (compact) Riemannian manifold (M, 〈⋅, ⋅〉), where G-structures are considered as sections of the quotient bundle (M)/G. We deduce the corresponding first and second variation formulae and the characterising conditions for critical points by means of tools closely related to the study of G-structures. In this direction, we show the rôle in the energy functional played by the intrinsic torsion of the G-structure. Moreover, we analyse the particular case G=U(n) for 2n-dimensional manifolds. This leads to the study of harmonic almost Hermitian manifolds and harmonic maps from M into (M)/U(n).

scholarly journals $$ \mathcal{N} $$ = 2 consistent truncations from wrapped M5-branes

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Davide Cassani ◽  
Grégoire Josse ◽  
Michela Petrini ◽  
Daniel Waldram
Keyword(s):  
Riemann Surface ◽  
Gauge Group ◽  
Tangent Bundle ◽  
Dimensional Manifold ◽  
Five Dimensions ◽  
Intrinsic Torsion ◽  
Consistent Truncations

Abstract We discuss consistent truncations of eleven-dimensional supergravity on a six-dimensional manifold M, preserving minimal $$ \mathcal{N} $$ N = 2 supersymmetry in five dimensions. These are based on GS ⊆ USp(6) structures for the generalised E6(6) tangent bundle on M, such that the intrinsic torsion is a constant GS singlet. We spell out the algorithm defining the full bosonic truncation ansatz and then apply this formalism to consistent truncations that contain warped AdS5×wM solutions arising from M5-branes wrapped on a Riemann surface. The generalised U(1) structure associated with the $$ \mathcal{N} $$ N = 2 solution of Maldacena-Nuñez leads to five-dimensional supergravity with four vector multiplets, one hypermultiplet and SO(3) × U(1) × ℝ gauge group. The generalised structure associated with “BBBW” solutions yields two vector multiplets, one hypermultiplet and an abelian gauging. We argue that these are the most general consistent truncations on such backgrounds.

Weak solutions of the Monge–Ampère equation on compact Hermitian manifolds

2017 ◽  
Vol 28 (09) ◽  
pp. 1740002
Author(s):  
Sławomir Kołodziej
Keyword(s):  
Weak Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Stability Of Solutions ◽  
Hermitian Manifolds ◽  
Priori Estimates ◽  
Existence And Stability ◽  
Monge Ampere

In this paper, we describe how pluripotential methods can be applied to study weak solutions of the complex Monge–Ampère equation on compact Hermitian manifolds. We indicate the differences between Kähler and non-Kähler setting. The results include a priori estimates, existence and stability of solutions.

scholarly journals Invariant torsion and G2-metrics

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Diego Conti ◽  
Thomas Bruun Madsen
Keyword(s):  
Local Homogeneity ◽  
Spinor Bundle ◽  
Intrinsic Torsion

AbstractWe introduce and study a notion of invariant intrinsic torsion geometrywhich appears, for instance, in connection with the Bryant-Salamon metric on the spinor bundle over S3. This space is foliated by sixdimensional hypersurfaces, each of which carries a particular type of SO(3)-structure; the intrinsic torsion is invariant under SO(3). The last condition is sufficient to imply local homogeneity of such geometries, and this allows us to give a classification. We close the circle by showing that the Bryant-Salamon metric is the unique complete metric with holonomy G2 that arises from SO(3)-structures with invariant intrinsic torsion.

scholarly journals On real bisectional curvature for Hermitian manifolds

2018 ◽  
Vol 371 (4) ◽  
pp. 2703-2718 ◽  
Author(s):  
Xiaokui Yang ◽  
Fangyang Zheng
Keyword(s):  
Bisectional Curvature ◽  
Hermitian Manifolds
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