collaborators

6 papers

math.DG2025

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…

math.DG2024

Nijenhuis operators on homogeneous spaces related to -algebras

Tomasz Goliński, 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…

math.DG2024

Nijenhuis operators on Banach homogeneous spaces

Tomasz Goliński, 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…

math.DG2024

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…

math.FA2024

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 $…

math.DG2024

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…