Results 121 to 130 of about 1,529 (146)

A non-Standard Indefinite Einstein Solvmanifold

Proceedings of the International Geometry Center
We describe an example of an indefinite invariant Einstein metric on a solvmanifold which is not standard, and whose restriction on the nilradical is ...
F. Rossi
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On the Canonical Bundle of Complex Solvmanifolds and Applications to Hypercomplex Geometry

Transformation groups, 2023
We study complex solvmanifolds $\Gamma\backslash G$ with holomorphically trivial canonical bundle. We show that the trivializing section of this bundle can be either invariant or non-invariant by the action of $G$.
A. Andrada, A. Tolcachier
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Three-step Harmonic Solvmanifolds

Geometriae Dedicata, 2003
The authors define a solvmanifold as a connected and simply connected solvable Lie group together with a left-invariant metric. Damek-Ricci spaces are examples of solvmanifolds. These spaces appeared as counter-examples for the Lichnerowicz conjecture, namely, that every harmonic Riemannian manifold would be locally isometric to a two-point homogeneous
Benson, Chal, Payne, Tracy L., Ratcliff, Gail   +2 more
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VAISMAN STRUCTURES ON LCK SOLVMANIFOLDS

Tsukuba Journal of Mathematics, 2023
An LCK manifold is a Hermitian manifold \((M,g,J)\) such that the fundamental \(2\)-form \(\Omega\), defined by \(\Omega(X,Y)=g(X,JY)\), satisfies the condition \(d\Omega= \omega\wedge \Omega\) for a closed 1-form \(\omega\). An LCK manifold is said to be Vaisman if \(\omega\) is parallel.
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Classification of 6-dimensional splittable flat solvmanifolds

Manuscripta mathematica, 2021
A flat solvmanifold is a compact quotient $$\Gamma \backslash G$$ Γ \ G where G is a simply-connected solvable Lie group endowed with a flat left invariant metric and $$\Gamma $$ Γ is a lattice of G . Any such Lie group can be written as $$G={\mathbb {R}}
A. Tolcachier
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FLOWS ON COMPACT SOLVMANIFOLDS

Mathematics of the USSR-Sbornik, 1985
Translation from Mat. Sb., Nov. Ser. 123(165), No.4, 549-558 (Russian) (1984; Zbl 0545.28013).
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A Holomorphic Bundle Criterion for Compactness of Pseudoconcave Solvmanifolds

Punjab University journal of mathematics
We prove that a pseudoconcave complex homogeneous space of a connected solvable linear algebraic group is necessarily compact. This resolves a central conjecture in the theory, showing that pseudoconcavity characterizes compactness for this large class ...
Raheel Farooki
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Six‐dimensional complex solvmanifolds with non‐invariant trivializing sections of their canonical bundle

Mathematische Nachrichten
It is known that there exist complex solvmanifolds (Γ∖G,J)$(\Gamma \backslash G,J)$ whose canonical bundle is trivialized by a holomorphic section that is not invariant under the action of G$G$ .
A. Tolcachier
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Special non-Kähler metrics on Endo–Pajitnov manifolds

Annali di Matematica Pura ed Applicata
We investigate the metric and cohomological properties of higher dimensional analogues of Inoue surfaces, that were introduced by Endo and Pajitnov. We provide a solvmanifold structure and show that in the diagonalizable case, they are formal and have ...
Cristian Ciulică, A. Otiman, Miron Stanciu   +2 more
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Characteristic Classes of Compact Solvmanifolds

The Annals of Mathematics, 1962
A solvmanifold (nilmanifold) is the homogeneous space of a connected solvable (nilpotent) Lie group. A theorem of A. I. Malcev [3] states that a nilmanifold can always be expressed as the quotient of a nilpotent Lie group by a discrete subgroup. From this it follows easily that nilmanifolds are parallelizable.
Auslander, Louis, Szczarba, R. H.
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