arXiv subjects

Giovane Galindo

Publications and source records attributed to Giovane Galindo.

4 recordsLinked to original sources

arXiv2025

Curvature positivity for Kähler and quasi-Kähler flag manifolds

In this paper, we study the notions of Griffiths and dual-Nakano positivity for the curvature of the Chern connection on Kähler and quasi-Kähler flag manifolds, as well as for the complex projective space. In this setting, we prove that every flag manifold endowed with a complex structure admits a metric of dual-Nakano semi-positive curvature, and we give a full classification of Kähler flag manifolds with Griffiths semi-positive curvature. Next we prove a series of restrictions for a quasi-Kähler flag manifold to have Griffiths semi-positive curvature, and we conjecture that in fact, there are no such metrics for non-integrable almost-complex structures. Lastly, we give a full classification on invariant metrics on the complex projective space with Griffiths and dual-Nakano semi-positive curvature.

math.DG↗

arXiv2025

Chern-Ricci flow and t-Gauduchon Ricci-flat condition

In this paper, we study the $t$-Gauduchon Ricci-flat condition under the Chern-Ricci flow. In this setting, we provide examples of Chern-Ricci flow on compact non-Kähler Calabi-Yau manifolds which do not preserve the $t$-Gauduchon Ricci-flat condition for $t<1$. The approach presented generalizes some previous constructions on Hopf manifolds. Also, we provide non-trivial new examples of balanced non-pluriclosed solution to the pluriclosed flow on non-Kähler manifolds. Further, we describe the limiting behavior, in the Gromov-Hausdorff sense, of geometric flows of Hermitian metrics (including the Chern-Ricci flow and the pluriclosed flow) on certain principal torus bundles over flag manifolds. In this last setting, we describe explicitly the Gromov-Hausdorff limit of the pluriclosed flow on principal $T^{2}$-bundles over the Fano threefold ${\mathbb{P}}(T_{{\mathbb{P}^{2}}})$.

math.DG↗

arXiv2024

Bundle type sub-Riemannian structures on holonomy bundles

In this paper, combining the Rashevsky-Chow-Sussmann (orbit) theorem with the Ambrose-Singer theorem, we introduce the notion of controllable principal connections on principal $G$-bundles. Using this concept, under a mild assumption of compactness, we estimate the Gromov-Hausdorff distance between principal $G$-bundles and certain reductive homogeneous $G$-spaces. In addition, we prove that every reduction of the structure group $G$ to a closed connected subgroup gives rise to a sequence of Riemannian metrics on the total space for which the underlying sequence of metric spaces converges, in the Gromov-Housdorff topology, to a normal reductive homogeneous $G$-space. This last finding allows one to detect the presence of certain reductive homogeneous $G$-spaces in the Gromov-Housdorff closure of the moduli space of Riemannian metrics of the total space of the bundle through topological invariants provided by obstruction theory.

math.DG↗

arXiv2021

The curvature of convex sum of metrics and applications

In this note, we derive explicit formulae for the curvature of a convex sum of Riemannian metrics, $g_t = (1-t)g_0 + t g_1$. We study whether such a deformation can increase the \emph{average} of the Riemann curvature component $R_t(X,Y,Y,X)$ along an immersed, totally geodesic flat torus. Because a first-order increase is prohibited, we obtain necessary and sufficient conditions for $g_t$ to have a positive average variation of order $r \geq 2$. These conditions are applied to paths joining $g_0$ to classical metric deformations, including conformal changes, vertical warpings, and Cheeger deformations.

math.DG↗