130,483 research outputs found
Cohomogeneity one Kaehler and Kaehler-Einstein manifolds with one singular orbit II
No full textPodesta and Spiro (Osaka J Math 36(4):805-833, 1999) introduced a class of G-manifolds M with a cohomogeneity one action of a compact semisimple Lie group G which admit an invariant Kahler structure (g, J) ("standard G-manifolds") and studied invariant Kahler and Kahler-Einstein metrics on M. In the first part of this paper, we gave a combinatoric description of the standard non-compact G-manifolds as the total space M-phi of the homogeneous vector bundle M = G x (H) V -> S-0 = G/ H over a flag manifold S-0 and we gave necessary and sufficient conditions for the existence of an invariant Kahler-Einstein metric g on such manifolds M in terms of the existence of an interval in the T-Weyl chamber of the flag manifold F = G x (H) PV which satisfies some linear condition. In this paper, we consider standard cohomogeneity one manifolds of a classical simply connected Lie group G = SUn, Sp(n).Spin(n) and reformulate these necessary and sufficient conditions in terms of easily checked arithmetic properties of the Koszul numbers associated with the flag manifold S-0 = G/H. If this condition is fulfilled, the explicit construction of the Kahler-Einstein metric reduces to the calculation of the inverse function to a given function of one variable
Almost complex submanifolds of a quaternionic Kaehler manifold.
No full textEditors: G. Pitis, G. Munteanu
Spectral properties of the twistor fibration of a quaternion K"ahler manifold
No full textAbstractOn a quaternion-Kähler manifold M the Hamiltonian of a Killing field is a 2-form and we show it is an eigenform of the Laplacian corresponding to the minimal eigenvalue. This gives a quaternionic version of a famous result of Lichnerowicz and Matsushima on Kähler–Einstein geometry.As a main tool we use the twistor fibration t:Z→M and establish some relations between the spectral geometries of Z and M
A twistor construction of (minimal) Kaehler submanifolds of a quaternionic Kaehler manifold
No full text
A twistor construction of Kaehler submanifolds of a quaternionic Kaehler manifold
No full textAbstract. A class of minimal almost complex submanifolds of a Riemannian manifold M ̃ 4n with a parallel quaternionic structure Q, in particular of a 4-dimensional oriented Riemannian manifold, is studied. A notion of Kähler submanifold is defined. Any Kähler submanifold is pluriminimal. In the case of a quaternionic Kähler manifold M ̃ 4n of non zero scalar curvature, in particular, when M ̃ 4 is an Einstein, non Ricci-flat, anti-self-dual 4-manifold, we give a twistor construction of Kähler submanifolds M2n of maximal possible dimension 2n.More precisely,we prove that any such Kähler submanifold M2n of M ̃ 4n is the projection of a holomorphic Legendrian submanifold L2n ? Z of the twistor space (Z,H) of M ̃ 4n , considered as a complex contact manifold with the natural holomorphic contact structure H ? TZ. Any Legendrian submanifold of the twistor space Z is defined by a generating holomorphic function. This is a natural generalization of Bryant’s construction of superminimal surfaces in S4 = HP1. Mathematics Subject Classification (1991). Primary: 53C40; Secondary: 53C5
Almost quaternionic Hermitian and quasi-Kaehler manifolds.
No full textEditors K. Sekigawa and S. Dimiev
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