arXiv subjects

Michaël Liefsoens

Publications and source records attributed to Michaël Liefsoens.

5 recordsLinked to original sources

arXiv2026

Curvature and Lagrangian submanifolds of the homogeneous nearly Kähler $\mathbb{C}P^3$

A tractable definition of the homogeneous nearly Kähler structure on $\mathbb{C}P^3$ is given via the Hopf fibration, facilitating explicit computations and analysis. The description extends to all homogeneous metrics on $\mathbb{C}P^3$, providing expressions for their Riemann curvature tensors and full isometry groups. Rigid immersions are presented for all extrinsically homogeneous Lagrangian submanifolds in the nearly Kähler $\mathbb{C}P^3$, and the nonexistence of Lagrangians with constant sectional curvature is established.

math.DG↗

arXiv2025

Classification results for totally real surfaces of nearly Kähler $\mathbb{C}P^3$

Totally real surfaces in the nearly Kähler $\mathbb{C}P^3$ are investigated and are completely classified under various additional assumptions, resulting in multiple new examples. Among others, the classification includes totally real surfaces that are extrinsically homogeneous; or minimal; or totally umbilical; or Codazzi-like (including parallel and non-parallel examples).

math.DG↗

arXiv2025

Hypersurfaces of any homogeneous $\mathbb{C}P^3$

Hypersurfaces are studied and classified under multiple additional assumptions in any Riemannian homogeneous space $(\mathbb{C}P^3, g_a)$, including nearly Kähler $\mathbb{C}P^3$. Notably, all extrinsically homogeneous hypersurfaces are classified in all these spaces, with an explicit family of examples. Moreover, for nearly Kähler $\mathbb{C}P^3$, all Hopf hypersurfaces are classified. Finally, Codazzi-like hypersurfaces (and in particular parallel and totally geodesic hypersurfaces), totally umbilical hypersurfaces and constant sectional curvature hypersurfaces are proven to not exist in any homogeneous $\mathbb{C}P^3$.

math.DG↗

arXiv2024

Isometry groups of nearly Kähler manifolds

Through the means of an alternative and less algebraic method, an explicit expression for the isometry groups of the six-dimensional homogeneous nearly Kähler manifolds is provided.

math.DG↗

arXiv2023

Spectral-based detection of chromatin loops in multiplexed super-resolution FISH data

Involved in mitotic condensation, interaction of transcriptional regulatory elements or isolation of structural domains, understanding loop formation is becoming a paradigm in the deciphering of chromatin architecture and its functional role. Despite the emergence of increasingly powerful genome visualization techniques, the high variability in cell populations and the randomness of conformations still make loop detection a challenge. We introduce a new approach for determining the presence and frequency of loops in a collection of experimental conformations obtained by multiplexed super-resolution imaging. Based on a spectral approach, in conjunction with neural networks, this method offers a powerful tool to detect loops in large experimental data sets, both at the population and single cell level. The method's performance is confirmed by applying it to recently published experimental data, where it provides a detailed and statistically quantified description of the global architecture of the chromosomal region under study.

q-bio.QM↗