arXiv subjects

Caio J. C. Negreiros

Publications and source records attributed to Caio J. C. Negreiros.

4 recordsLinked to original sources

arXiv2020

Geodesic orbit spaces in real flag manifolds

We describe the invariant metrics on real flag manifolds and classify those with the following property: every geodesic is the orbit of a one-parameter subgroup. Such a metric is called g.o. (geodesic orbit). In contrast to the complex case, on real flag manifolds the isotropy representation can have equivalent submodules, which makes invariant metrics depend on more parameters and allows us to find more cases in which non-trivial g.o. metrics exist.

math.DG↗

arXiv2016

Invariant almost complex geometry on flag manifolds: geometric formality and Chern numbers

In the first part of this paper we study geometric formality for generalized flag manifolds, including full flag manifolds of exceptional Lie groups. In the second part we deal with the problem of the classification of invariant almost complex structures on generalized flag manifolds using topological methods.

math.DG↗

arXiv2011

Equigeodesics on full, $G_2$ and a rank-three condition on flag manifolds

This paper provides a characterization and examples of homogeneous geodesics on full $G/T$ and $G_{2}$ flag manifolds. We discuss for generalized root systems the property of sum-zero triple of $T$-roots and give several applications of this result.

math.DG↗

arXiv2009

Equigeodesics on flag manifolds

This paper provides a characterization of homogeneous curves on a geometric flag manifold which are geodesic with respect to any invariant metric. We call such curves homogeneous equigeodesics. We also characterize homogeneous equigeodesics whose associated Killing field is closed, hence, the corresponding geodesics is closed.

math.DG↗