منابع مشابه
Tessellations of Solvmanifolds
Let A be a closed subgroup of a connected, solvable Lie group G, such that the homogeneous space A\G is simply connected. As a special case of a theorem of C. T. C. Wall, it is known that every tessellation A\G/Γ of A\G is finitely covered by a compact homogeneous space G′/Γ′. We prove that the covering map can be taken to be very well behaved — a “crossed” affine map. This establishes a connec...
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The purpose of the present expository paper is to give an account of the recent progress and present status of the classification of solvable Lie groups admitting an Einstein left invariant Riemannian metric, the only known examples so far of noncompact Einstein homogeneous manifolds. The problem turns to be equivalent to the classification of Ricci soliton left invariant metrics on nilpotent L...
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In this note we want to study compact homogeneous spaces G/Γ, where G is a connected and simply-connected Lie group and Γ a discrete subgroup in G. It is well known that the existence of such a Γ implies the unimodularity of the Lie group G. Recall that a Lie group G is called unimodular if for all X ∈ g holds tr adX = 0, where g denotes the Lie algebra of G. If we further demand G/Γ to be symp...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1998
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-98-01980-1