2 citations · 4 across the 14 of their papers we have counts for
15 papers
Retro-synthetic Riemannian geometry in Rocq I : Taylor series of a metric
Gabriella Clemente, Hugo Herbelin, Carlos Simpson
We introduce a synthetic framework for doing local Riemannian geometry that is influenced by a reverse-engineering method for formalizing in Rocq. These new perspectives and techni…
Differential Homology
Fabio Ferrari Ruffino, Gabriel Longatto Clemente
We first construct the differential refinement of singular homology, verifying that it satisfies the axioms dual to their cohomological counterparts. Then, we define the differenti…
Kähler thresholds
Gabriella Clemente, Carlos Simpson
The topology of Kähler manifolds is largely determined by the geometry due to its rigidity. In particular, the cohomology and Hodge theory of compact Kähler manifolds is quite rest…
Synthetic Differential Geometry in Lean
Riccardo Brasca, Gabriella Clemente
This article is about the formalization of synthetic differential geometry with the Lean proof assistant and the mathematical library mathlib. The main result we prove and formaliz…
Real Einstein loci
Gabriella Clemente
The aim of this article is to study the interplay between the complex, and underlying real geometries of a Kähler manifold. We provide a necessary and sufficient condition for cert…
Geometric structures as variational objects, II
Gabriella Clemente
This note is the sequel of "Geometric structures as variational objects, I." It generalizes the main result and perspectives of that work to a class of geometric structures that in…
Geometric structures as variational objects, I
Gabriella Clemente
This note provides a variational description of the most basic differential geometric structures on a smooth manifold.
A curvature obstruction to integrability
Gabriella Clemente
The classical theory of -structures, which include almost-complex structures, explains the relationship between the curvature of compatible connections and integrability. This n…
Curvature, integrability, and the six sphere
Gabriella Clemente
This note is about the interplay between the almost-hermitian and Riemannian geometries of a manifold. These geometries can be seen to interact through curvature. The main result i…
An extended Kodaira Spencer functional
Gabriella Clemente
This note is about an extension of the Kodaira-Spencer functional to Calabi-Yau manifolds of any dimension.
Complex structures as critical points
Gabriella Clemente
This note aims at obtaining a variational characterization of complex structures by means of a calculus of variations for real vector bundle valued differential forms, and outlines…
Functionals on the space of almost complex stuctures
Gabriella Clemente
We study functionals on the space of almost complex structures on a compact -manifold, whose variational properties could be used to tackle Yau's Challenge.
A technical remark on the Donaldson-Futaki invariant for Fano reductive group compactifications
Gabriella Clemente
We present an elementary way of recovering a well-known criterion of K-stability for Fano reductive group compactifications.
Geometry of universal embedding spaces for almost complex manifolds
Gabriella Clemente
We study the geometry of universal embedding spaces for compact almost complex manifolds of a given dimension. These spaces are complex algebraic analogues of twistor spaces that w…
Graphs with minimal well-covered dimension
Gabriella Clemente
There is a class of graphs with well-covered dimension equal to the simplicial clique number that contains all chordal graphs and infinitely many other graphs. These graphs general…