6 papers
Lie groups with a bi-invariant distance
Gabriel Larotonda, Iván Rey
We show that a Lie group admitting a bi-invariant distance must be the product of an abelian group and a compact group with discrete center. Moreover, the…
Nijenhuis operators on homogeneous spaces related to -algebras
Tomasz GoliÅski, Gabriel Larotonda, Alice Barbora Tumpach
For a unital non-simple -algebra we consider its Banach--Lie group of invertible elements. For a given closed ideal in , we consider…
Nijenhuis operators on Banach homogeneous spaces
Tomasz GoliÅski, Gabriel Larotonda, Alice Barbora Tumpach
For a Banach--Lie group and an embedded Lie subgroup we consider the homogeneous Banach manifold . In this context we establish the most general conditions…
Connections and Finsler geometry of the structure group of a JB-algebra
Gabriel Larotonda, José Luna
We endow the Banach-Lie structure group of an infinite dimensional JB-algebra with a left-invariant connection and Finsler metric, and we compute all the quantities of…
Convexity of sums of eigenvalues of a segment of unitaries
Gabriel Larotonda, Martin Miglioli
For a unitary matrix with skew-Hermitian, the angles of are the arguments of its spectrum, i.e. the spectrum of . For , we show that $…
Totally geodesic submanifolds in the manifold SPD of symmetric positive-definite real matrices
Alice Barbara Tumpach, Gabriel Larotonda
This paper is a self-contained exposition of the geometry of symmetric positive-definite real matrices , including necessary and sufficent condit…