6 papers · 1 filter
First Laplace eigenvalue of strongly isotropy irreducible spaces
Emilio A. Lauret, Fiorela Rossi Bertone, Alejandro Tolcachier
We study the smallest positive eigenvalue of the Laplace-Beltrami operator associated with any compact strongly isotropy irreducible space. We provide an explicit expression…
Six-dimensional complex solvmanifolds with non-invariant trivializing sections of their canonical bundle
Alejandro Tolcachier
It is known that there exist complex solvmanifolds whose canonical bundle is trivialized by a holomorphic section which is not invariant under the action of $G…
Linear stability of Perelman's -entropy of standard Einstein manifolds
Emilio A. Lauret, Alejandro Tolcachier
Paul Schwahn recently exhibited 112 non-symmetric, connected, simply connected, compact Einstein manifolds that are stable with respect to the total scalar curvature functional res…
Hypercomplex structures on special linear groups
Adrián Andrada, AgustÃn Garrone, Alejandro Tolcachier
The purpose of this article is twofold. First, we prove that the -dimensional Lie group does not admit a left-invariant hypercomplex structure.…
Harmonic almost complex structures on almost abelian Lie groups and solvmanifolds
Adrián Andrada, Alejandro Tolcachier
An almost abelian Lie group is a solvable Lie group with a codimension-one normal abelian subgroup. We characterize almost Hermitian structures on almost abelian Lie groups where t…
On the canonical bundle of complex solvmanifolds and applications to hypercomplex geometry
Adrián Andrada, Alejandro Tolcachier
We study complex solvmanifolds with holomorphically trivial canonical bundle. We show that the trivializing section of this bundle can be either invariant or non-i…