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Locally conformally Kähler solvmanifolds: a survey [PDF]
Complex Manifolds, 2019 A Hermitian structure on a manifold is called locally conformally Kähler (LCK) if it locally admits a conformal change which is Kähler. In this survey we review recent results of invariant LCK structures on solvmanifolds and present original results ...
Andrada A., Origlia M.
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Uniform distribution in solvmanifolds
Advances in Mathematics, 1971 L. Auslander, Jonathan Brezin
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A note on compact solvmanifolds with Kahler structures [PDF]
Osaka Journal of Mathematics, 2004 In this note we show that a compact solvmanifold admits a Kstructure if and only if it is a finite quotient of a complex torus which has a structure of a com- plex torus bundle over a complex torus.
K. Hasegawa
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Pseudo-Riemannian Sasaki solvmanifolds [PDF]
, 2022 We study a class of left-invariant pseudo-Riemannian Sasaki metrics on solvable Lie groups, which can be characterized by the property that the zero level set of the moment map relative to the action of some one-parameter subgroup $\{\exp tX\}$ is a normal nilpotent subgroup commuting with $\{\exp tX\}$, and $X$ is not lightlike.
Diego Conti +2 more
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The Anosov theorem for exponential solvmanifolds [PDF]
Pacific Journal of Mathematics, 1995 The authors exhibit a class \({\mathcal N} {\mathcal R}\) of compact solvmanifolds such that for any \(S \in {\mathcal N} {\mathcal R}\) and any selfmap \(f : S \to S\) the Nielsen number \(N(f)\) equals the absolute value \(|L(f) |\) of the Lefschetz number.
Edward C. Keppelmann, Christopher McCord
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Cohomologically symplectic solvmanifolds are symplectic [PDF]
Journal of Symplectic Geometry, 2011 We consider aspherical manifolds with torsion-free virtually polycyclic fundamental groups, constructed by Baues. We prove that if those manifolds are cohomologically symplectic then they are symplectic. As a corollary we show that cohomologically symplectic solvmanifolds are symplectic.
Hisashi Kasuya
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Infra-solvmanifolds of dimension four [PDF]
Bulletin of the Australian Mathematical Society, 2000 The article states some results obtained by the author in his thesis: The author considers compact 4-manifolds that are the quotient of some simply connected solvable Lie group \(S\) by an isometric action of a group \(\Gamma\). When \(S\) is solvable it has been shown that the isomorphism class of the fundamental group of such a manifold determines ...
Robin J. Cobb
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Tessellations of solvmanifolds [PDF]
Transactions of the American Mathematical Society, 1998 Let A A be a closed subgroup of a connected, solvable Lie group G G , such that the homogeneous space A ∖ G A\backslash G is simply connected. As a special case of a theorem of C. T. C. Wall, it is known that every tessellation A ∖ G /
Dave Witte, Dave Witte
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Weyl-Einstein structures on conformal solvmanifolds [PDF]
Geometriae Dedicata, 2022 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 left-invariant metric g on M. We study Weyl-Einstein structures on conformal solvable Lie groups and on their compact
Viviana del Barco +2 more
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On Some Structural Components of Nilsolitons
Mathematical Problems in Engineering, Volume 2021, Issue 1, 2021., 2021 In this paper, we study nilpotent Lie algebras that admit nilsoliton metric with simple pre‐Einstein derivation. Given a Lie algebra η, we would like to compute as much of its structure as possible. The structural components we consider in this study are the structure constants, the index, and the rank of the nilsoliton derivations.
Hulya Kadioglu, Mustafa Inc
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