arXiv subjects

Rafaela F. do Prado

Publications and source records attributed to Rafaela F. do Prado.

3 recordsLinked to original sources

arXiv2022

Geodesics on adjoint orbits of $SL(n, \mathbb{R})$

In this paper we study geodesics on adjoint orbits of $SL(n,\mathbb{R})$ equipped with $SO(n)$-invariant metrics (maximal compact subgroup). Our main technique is translate this problem into a geometric problem in the tangent bundle of certain $SO(n)$-flag manifolds and describe the geodesics equations with respect to the Sasaki metric on tangent bundle. We also use tools of Lie Theory in order to obtain some explicit description of families of geodesics. We deal with the case of $SL(2,\mathbb{R})$ in full details.

math.DG↗

arXiv2017

On the stability of harmonic maps under the homogeneous Ricci flow

In this work we study properties of stability and non-stability of harmonic maps under the homogeneous Ricci flow. We provide examples where the stability (non-stability) is preserved under the Ricci flow and an example where the Ricci flow does not preserve the stability of an harmonic map.

math.DG↗

arXiv2016

Variational aspects of homogeneous geodesics on generalized flag manifolds and applications

We study conjugate points along homogeneous geodesics in generalized flag manifolds. This is done by analyzing the second variation of the energy of such geodesics. We also give an example of how the homogeneous Ricci flow can evolve in such way to produce conjugate points in the complex projective space $\mathbb{C} P^{2n+1} = Sp(n+1)/({U}(1)\times{Sp}(n))$.

math.DG↗