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The mean curvature flow on solvmanifolds
This work is a survey of the most relevant background material to motivate and understand the construction and classification of translating...
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Hypercomplex Almost Abelian Solvmanifolds
We give a characterization of almost abelian Lie groups carrying left invariant hypercomplex structures and we show that the corresponding Obata...
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Remarks on Some Compact Symplectic Solvmanifolds
We study the hard Lefschetz property on compact symplectic solvmanifolds, i.e., compact quotients M = Γ G of a simply-connected solvable Lie group G ...
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An averaging formula for Nielsen numbers on infra-solvmanifolds
Until now only for special classes of infra-solvmanifolds, namely, infra-nilmanifolds and infra-solvmanifolds of type ( R ), there was a formula...
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A Construction of Einstein Solvmanifolds not Based on Nilsolitons
We construct indefinite Einstein solvmanifolds that are standard, but not of pseudo-Iwasawa type. Thus, the underlying Lie algebras take the form
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Harmonic almost complex structures on almost abelian Lie groups and solvmanifolds
An almost abelian Lie group is a solvable Lie group with a codimension one normal abelian subgroup. We characterize almost Hermitian structures on...
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On the rationality of the Nielsen zeta function for maps on solvmanifolds
In Dekimpe and Dugardein (J Fixed Point Theory Appl 17:355–370, 2015), Fel’shtyn and Lee (Topol Appl 181:62–103, 2015), the Nielsen zeta function
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Critical metrics for quadratic curvature functionals on some solvmanifolds
We prove the existence of four-dimensional compact manifolds admitting some non-Einstein Lorentzian metrics, which are critical points for all...
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Pseudo-Kähler and pseudo-Sasaki structures on Einstein solvmanifolds
The aim of this paper is to construct left-invariant Einstein pseudo-Riemannian Sasaki metrics on solvable Lie groups. We consider the class of
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Locally conformally product structures on solvmanifolds
We study left invariant locally conformally product structures on simply connected Lie groups and give their complete description in the solvable...
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Nielsen coincidence theory on infra-solvmanifolds of Sol
We derive averaging formulas for the Lefschetz coincidence numbers, the Nielsen coincidence numbers and the Reidemeister coincidence numbers of maps...
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Weyl-Einstein structures on conformal solvmanifolds
A conformal Lie group is a conformal manifold ( M , c ) such that M has a Lie group structure and c is the conformal structure defined by a...
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Holonomy groups of compact flat solvmanifolds
In this article we study the holonomy groups of flat solvmanifolds. It is known that the holonomy group of a flat solvmanifold is abelian; we give an...
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Distinguished \(G_2\) -Structures on Solvmanifolds
Among closed \(G_2\)-structures there are two very distinguished classes: Laplacian solitons and Extremally Ricci-pinched \(G_2\)-structures. We...
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New pseudo Einstein metrics on Einstein solvmanifolds
A Riemannian Einstein manifold is called an Einstein solvmanifold if there exists a transitive solvable group of isometries. In this short note, we...
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ALMOST ABELIAN LIE GROUPS, SUBGROUPS AND QUOTIENTS
An almost Abelian Lie group is a non-Abelian Lie group with a codimension 1 Abelian normal subgroup. The majority of 3-dimensional real Lie groups...