Results 21 to 30 of about 65 (63)
Distinguished $$G_2$$-Structures on Solvmanifolds [PDF]
, 2020 Among closed G2-structures there are two very distinguished classes: Laplacian solitons and Extremally Ricci-pinched G2-structures. We study the existence problem and explore possible interplays between these concepts in the context of left-invariant G2-structures on solvable Lie groups.
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Global regularity on 3-dimensional solvmanifolds [PDF]
Transactions of the American Mathematical Society, 1992 Let M M be any 3 3 -dimensional (nonabelian) compact solvmanifold. We apply the methods of representation theory to study the convergence of Fourier series of smooth global solutions to first order invariant partial differential equations D f = g Df = g in
Cygan, Jacek M., Richardson, Leonard F.
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The Classification of Flat Solvmanifolds [PDF]
Transactions of the American Mathematical Society, 1978 This paper contains a complete algebraic characterization of the fundamental groups of flat solvmanifolds. This characterization is in terms of finite integral representations of free abelian groups and the associated cohomology. A classification of compact flat solvmanifolds follows, and a list of all compact flat solvmanifolds of dimensions 3, 4, and
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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 /
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On line bundles arising from the LCK structure over locally conformal Kähler solvmanifolds
Complex ManifoldsWe can construct a real line bundle arising from the locally conformal Kähler (LCK) structure over an LCK manifold. We study the properties of this line bundle over an LCK solvmanifold whose complex structure is left-invariant. Mainly, we prove that this
Yamada Takumi
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Strong Kähler with torsion solvable lie algebras with codimension 2 nilradical
Mathematische Nachrichten, Volume 297, Issue 12, Page 4705-4729, December 2024.Abstract In this paper, we study strong Kähler with torsion (SKT) and generalized Kähler structures on solvable Lie algebras with (not necessarily abelian) codimension 2 nilradical. We treat separately the case of J$J$‐invariant nilradical and non‐J$J$‐invariant nilradical. A classification of such SKT Lie algebras in dimension 6 is provided.
Beatrice Brienza, Anna Fino
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Inhomogeneous deformations of Einstein solvmanifolds
Journal of the London Mathematical Society, Volume 109, Issue 5, May 2024.Abstract For each non‐flat, unimodular Ricci soliton solvmanifold (S0,g0)$(\mathsf {S}_0,g_0)$, we construct a one‐parameter family of complete, expanding, gradient Ricci solitons that admit a cohomogeneity one isometric action by S0$\mathsf {S}_0$. The orbits of this action are hypersurfaces homothetic to (S0,g0)$(\mathsf {S}_0,g_0)$.
Adam Thompson
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Ricci soliton solvmanifolds [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2011 18 pages, to appear in Crelle's ...
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Compact CR-solvmanifolds as Kähler obstructions [PDF]
Mathematische Zeitschrift, 2010 We give a precise characterization for when a compact CR-solvmanifold is CR-embeddable in a complex Kähler manifold. Equivalently this gives a non-Kähler criterion for complex manifolds containing CR-solvmanifolds not satisfying these conditions. This paper is the natural continuation of Oeljeklaus and Richthofer [J Differ Geom 27(3):399-421, 1988] and
Gilligan, Bruce, Oeljeklaus, Karl
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Supersymmetric scale-separated AdS3 orientifold vacua of type IIB
Journal of High Energy PhysicsI construct supersymmetric AdS3 vacua of type IIB string theory that exhibit parametric scale separation in the controlled regime. These solutions arise from compactifications on seven-dimensional manifolds equipped with co-closed G 2-structures, in the ...
Vincent Van Hemelryck
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