2 citations · 4 across the 14 of their papers we have counts for
8 papers · 1 filter
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…
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…
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.