Benjamin Aslan
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Calibrated geometry in hyperkähler cones, 3-Sasakian manifolds, and twistor spaces Open
We systematically study calibrated geometry in hyperkähler cones $C^{4n+4}$ , their 3-Sasakian links $M^{4n+3}$ , and the corresponding twistor spaces $Z^{4n+2}$ , emphasizing the relationships between submanifold geometries in various spa…
Calibrated Geometry in Hyperkahler Cones, 3-Sasakian Manifolds, and Twistor Spaces Open
We systematically study calibrated geometry in hyperkähler cones $C^{4n+4}$, their 3-Sasakian links $M^{4n+3}$, and the corresponding twistor spaces $Z^{4n+2}$, emphasizing the relationships between submanifold geometries in various spaces…
On $G_2$ manifolds with cohomogeneity two symmetry Open
We consider $G_2$ manifolds with a cohomogeneity two $\mathbb{T}^2\times \mathrm{SU}(2)$ symmetry group. We give a local characterization of these manifolds and we describe the geometry, including regularity and singularity analysis, of co…
Special Lagrangians in nearly Kähler $\mathbb{CP}^3$ Open
This article explores special Lagrangian submanifolds in $\mathbb{CP}^3$, viewed as a nearly Kähler manifold, from two different perspectives. Intrinsically, using a moving frame set-up, and extrinsically, using $\mathrm{SU}(2)$ moment-typ…
View article: Group invariant machine learning by fundamental domain projections
Group invariant machine learning by fundamental domain projections Open
We approach the well-studied problem of supervised group invariant and equivariant machine learning from the point of view of geometric topology. We propose a novel approach using a pre-processing step, which involves projecting the input …