https://neckpinch.com/authors/julieth-saavedra/New arXiv papers by Julieth Saavedra, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.02519arxiv:2610.02519Thu, 01 Oct 2026 00:00:00 GMTAnna Fino, Julieth Saavedra — We study almost Hermitian manifolds whose lowered Nijenhuis tensor is totally skew-symmetric and whose characteristic (Bismut) torsion is closed, the almost-SKT condition. This extends the SKT (pluriclosed) condition beyond the integrable setting. For a fixed almost complex structure, these constraints are linear in the metric. We introduce an overdetermined ellipticity condition which, on compact manifolds, makes the admissible infinitesimal deformation space finite-dimensional and yields short-time existence for a constrained Bismut–Ricci flow. In real dimension six, almost-SKT structures satisfy a dichotomy: either the almost complex structure is integrable, or the skew Nijenhuis tensor is nowhere vanishing with constant norm and the Bismut Ricci form vanishes. Hence, on compact non-integrable almost-SKT six-manifolds, the constrained Bismut–Ricci flow is stationary. In dimension eight, ellipticity always fails, while in higher dimensions Nijenhuis rigidity holds on an open dense locus. In arbitrary dimension, we characterize when total skew-symmetry of the lowered Nijenhuis tensor determines the compatible metric pointwise up to scale. On compact manifolds, with closed torsion, this implies uniqueness of the almost-SKT metric up to scaling; the constrained Bismut–Ricci flow is then an explicit homothetic solution. We also relate this flow to generalized Ricci flow and characterize the infinitesimal obstruction to lifting the evolution when the almost complex structure varies. Finally, we construct non-integrable almost-SKT structures with nowhere vanishing Nijenhuis tensor and non-flat characteristic connection on compact six-manifolds, including S¹× S²× S³ and S³× S³. In these families, the metric is fixed and the compatible almost complex structures form an S²-family. These structures have vanishing Bismut Ricci form and are therefore almost-CYT.Ricci flowGeneralized & G₂ flowsStability & uniquenessHarmonic maps & DeTurck trick https://arxiv.org/abs/2406.15254arxiv:2406.15254Fri, 21 Jun 2024 00:00:00 GMTHenrique N. Sá Earp, Julieth Saavedra, Caleb Suan — We explore three versions of the Laplacian coflow of G₂-structures on circle fibrations over Calabi–Yau 3-folds, interpreting their dimensional reductions to the Kähler geometry of the base. Precisely, we reduce Ansätze for the Laplacian coflow, modified or not by de Turck's trick, both on trivial products CY³× S¹ and on contact Calabi–Yau 7-manifolds, obtaining in each case a natural modification of the Kähler–Ricci flow.Ricci flowKähler–Ricci flowGeneralized & G₂ flowsRicci-flat & Calabi–Yau3-manifoldsKähler geometryHarmonic maps & DeTurck trick https://arxiv.org/abs/2401.02805arxiv:2401.02805Fri, 05 Jan 2024 00:00:00 GMTBrian Grajales, Gabriel Rondón, Julieth Saavedra — In this paper, we investigate homogeneous Riemannian geometry on real flag manifolds of the split real form of g₂. We characterize the metrics that are invariant under the action of a maximal compact subgroup of G₂. Our exploration encompasses the analysis of g.o. metrics and equigeodesics on the g₂-type flag manifolds. Additionally, we explore the Ricci flow for the case where the isotropy representation has no equivalent summands, employing techniques from the qualitative theory of dynamical systems.Ricci flowHomogeneous spaces