Results 81 to 90 of about 1,208 (130)
Remarks on some compact symplectic solvmanifolds [PDF]
arXiv, 2020 We study the hard Lefschetz property on compact symplectic solvmanifolds, i.e., compact quotients $M=\Gamma\backslash G$ of a simply-connected solvable Lie group $G$ by a lattice $\Gamma$, admitting a symplectic structure.
arxiv
Maximal symmetry and unimodular solvmanifolds [PDF]
Pacific Journal of Mathematics, 2019 Recently, it was shown that Einstein solvmanifolds have maximal symmetry in the sense that their isometry groups contain the isometry groups of any other left-invariant metric on the given Lie group. Such a solvable Lie group is necessarily non-unimodular.
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The mean curvature flow on solvmanifolds
Boletín de la Sociedad Matemática MexicanaThis work is a survey of the most relevant background material to motivate and understand the construction and classification of translating solutions to mean curvature flow on a family of solvmanifolds. We introduce the mean curvature flow and some known results in the field.
Romina M. Arroyo +3 more
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An Averaging Formula for Nielsen numbers on Infra-Solvmanifolds [PDF]
arXiv, 2020 Until now only for special classes of infra-solvmanifolds, namely infra-nilmanifolds and infra-solvmanifolds of type (R), there was a formula available for computing the Nielsen number of a self-map on those manifolds. In this paper, we provide a general averaging formula which works for all self-maps on all possible infra-solvmanifolds and which ...
arxiv
Einstein solvmanifolds and nilsolitons
, 2008 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.
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Small deformations and non-left-invariant complex structures on a compact solvmanifold [PDF]
Differential Geometry and its Applications, Vol. 28, 220-227
(2010), 2007 We observed in our previous paper that all the complex structures on four-dimensional compact solvmanifolds, including tori, are left-invariant. In this paper we will give an example of a six-dimensional compact solvmanifold which admits a continuous family of non-left-invariant complex structures. Furthermore, we will make a complete classification of
arxiv
Some Compact Solvmanifolds and Locally Affine Spaces [PDF]
, 1958 Louis Auslander
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On the structure of complex solvmanifolds [PDF]
Journal of Differential Geometry, 1988 Oeljeklaus, Karl, Richthofer, Wolfgang
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Generalized deformations and holomorphic Poisson cohomology of solvmanifolds [PDF]
arXiv, 2012 We describe the generalized Kuranishi spaces of solvmanifolds with left-invariant complex structures. By using such description, we study the stability of left-invariantness of deformed generalized complex structures and smoothness of generalized Kuranishi spaces on certain classes of solvmanifolds.
arxiv