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Classification of invariant AHS-structures on semisimple locally symmetric spaces

100%
Gregorovič J.
Open Mathematics
|
2013
|
tom 11
|
nr 12
2062-2075
EN
We discuss which semisimple locally symmetric spaces admit an AHS-structure invariant under local symmetries. We classify them for all types of AHS-structures and determine possible equivalence classes of such AHS-structures.
2
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On the characteristic connection of gwistor space

64%
Albuquerque R.
Open Mathematics
|
2013
|
tom 11
|
nr 1
149-160
EN
We give a brief presentation of gwistor spaces, which is a new concept from G 2 geometry. Then we compute the characteristic torsion T c of the gwistor space of an oriented Riemannian 4-manifold with constant sectional curvature k and deduce the condition under which T c is ∇c-parallel; this allows for the classification of the G 2 structure with torsion and the characteristic holonomy according to known references. The case of an Einstein base manifold is envisaged.
3
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Affine compact almost-homogeneous manifolds of cohomogeneity one

52%
Guan D.
Open Mathematics
|
2009
|
tom 7
|
nr 1
84-123
EN
This paper is one in a series generalizing our results in [12, 14, 15, 20] on the existence of extremal metrics to the general almost-homogeneous manifolds of cohomogeneity one. In this paper, we consider the affine cases with hypersurface ends. In particular, we study the existence of Kähler-Einstein metrics on these manifolds and obtain new Kähler-Einstein manifolds as well as Fano manifolds without Kähler-Einstein metrics. As a consequence of our study, we also give a solution to the problem posted by Ahiezer on the nonhomogeneity of compact almost-homogeneous manifolds of cohomogeneity one; this clarifies the classification of these manifolds as complex manifolds. We also consider Fano properties of the affine compact manifolds.
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