cohomogeneity one action
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Author(s):  
Izar Alonso ◽  
Francesca Salvatore

AbstractWe consider balanced metrics on complex manifolds with holomorphically trivial canonical bundle, most commonly known as balanced SU(n)-structures. Such structures are of interest for both Hermitian geometry and string theory, since they provide the ideal setting for the Hull–Strominger system. In this paper, we provide a non-existence result for balanced non-Kähler $$\text {SU}(3)$$ SU ( 3 ) -structures which are invariant under a cohomogeneity one action on simply connected six-manifolds.



2019 ◽  
pp. 1-21
Author(s):  
Fabio Podestà

Abstract We prove the existence of a one-parameter family of nearly parallel G2-structures on the manifold $\text{S}^{3}\times \mathbb{R}^{4}$ , which are mutually non-isomorphic and invariant under the cohomogeneity one action of the group SU(2)3. This family connects the two locally homogeneous nearly parallel G2-structures that are induced by the homogeneous ones on the sphere S7.



2019 ◽  
Vol 203 (1) ◽  
pp. 205-223
Author(s):  
Jeffrey D. Carlson ◽  
Oliver Goertsches ◽  
Chen He ◽  
Augustin-Liviu Mare


2019 ◽  
Vol 31 (1) ◽  
pp. 265-273
Author(s):  
Fabio Podestà ◽  
Alberto Raffero

Abstract We prove that the automorphism group of a compact 6-manifold M endowed with a symplectic half-flat {\mathrm{SU}(3)} -structure has Abelian Lie algebra with dimension bounded by {\min\{5,b_{1}(M)\}} . Moreover, we study the properties of the automorphism group action and we discuss relevant examples. In particular, we provide new complete examples on {T\mathbb{S}^{3}} which are invariant under a cohomogeneity one action of {\mathrm{SO}(4)} .



1999 ◽  
Vol 10 (05) ◽  
pp. 541-570 ◽  
Author(s):  
ANDREW DANCER ◽  
ANDREW SWANN

Classification results are given for (i) compact quaternionic Kähler manifolds with a cohomogeneity-one action of a semi-simple group, (ii) certain complete hyperKähler manifolds with a cohomogeneity-two action of a semi-simple group preserving each complex structure, (iii) compact 3-Sasakian manifolds which are cohomogeneity one with respect to a group of 3-Sasakian symmetries. Information is also obtained about non-compact quaternionic Kähler manifolds of cohomogeneity one and the cohomogeneity of adjoint orbits in complex semi-simple Lie algebras.



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