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Weak Fan Structures for Two-Parameter Degenerations of K3 Surfaces
Badre Mounda
https://arxiv.org/abs/2507.14954 https://arxiv.org/pd…

Weak Fan Structures for Two-Parameter Degenerations of K3 Surfaces
In this note, we provide an explicit computation of the weak fan associated with a two-parameter degeneration of K3 surfaces. This example serves as a concrete illustration of the general framework developed by Robles and Deng (2023) for the compactification of period maps via nilpotent orbits in the non-Hermitian case. We describe the associated nilpotent cones, examine their compatibility conditions, and construct the weak fan governing the degeneration behavior. This computation contributes …

Geometry of left-invariant vector fields on Lie groups
M. L. Foka, R. P. Nimpa, M. B. N. Djiadeu
https://arxiv.org/abs/2508.11440 https://arxiv.org/pdf/250…

Geometry of left-invariant vector fields on Lie groups
This paper examines the geometry of left-invariant vector fields on five-dimensional, simply connected, nilpotent Lie groups equipped with left-invariant Riemannian metrics. Using the canonical identification between the Lie algebra and the space of left-invariant vector fields, we derive algebraic characterizations for Killing, one-harmonic Killing, conformal, and concurrent vector fields. Employing a classification of these nilpotent Lie algebras into ten canonical types, we perform a case-by…