arXiv subjects

Elahe Khalili Samani

Publications and source records attributed to Elahe Khalili Samani.

6 recordsLinked to original sources

arXiv2026

Positive intermediate Ricci curvature on cohomogeneity one manifolds in low dimensions

We explore existence of invariant metrics with positive intermediate Ricci curvature on closed, low-dimensional cohomogeneity one manifolds. For a certain cohomogeneity one $\mathsf{Spin}(4)$-action on $S^3 \times \mathbb{C}\mathrm{P}^2$, we construct an invariant metric with positive 4th-intermediate Ricci curvature and show it cannot admit an invariant metric with positive 3rd-intermediate Ricci curvature. We further establish similar symmetry obstructions to positive curvature for $S^3 \times S^3$, $S^3 \times S^4$, and several families of cohomogeneity one manifolds.

math.DG↗

arXiv2025

Positive curvature and rational ellipticity in cohomogeneity three

We prove that a closed, simply connected, positively curved, cohomogeneity-three manifold whose quotient space has no boundary is rationally elliptic, thus providing a generalization of similar results regarding rational ellipticity of homogeneous, cohomogeneity-one, and almost non-negatively curved cohomogeneity-two manifolds.

math.DG↗

arXiv2024

Rational ellipticity of $G$-manifolds from their quotients

We prove that if a compact, simply connected Riemannian $G$-manifold $M$ has orbit space $M/G$ isometric to some other quotient $N/H$ with $N$ having zero topological entropy, then $M$ is rationally elliptic. This result, which generalizes most conditions on rational ellipticity, is a particular case of a more general result involving manifold submetries.

math.DG↗

arXiv2024

Positive curvature and discrete abelian symmetry

By replacing the torus with an elementary abelian two-group, we generalize the maximal symmetry result of Grove and Searle and the half-maximal symmetry result of Wilking for positively curved manifolds with an isometric torus action.

math.DG↗

arXiv2022

On the topology of leaves of singular Riemannian foliations

In this paper, we establish a number of results about the topology of the leaves of a closed singular Riemannian foliation $(M,\fol)$. If $M$ is simply connected, we prove that the leaves are finitely covered by nilpotent spaces, and characterize the fundamental group of the generic leaves. If $M$ has virtually nilpotent fundamental group, we prove that the leaves have virtually nilpotent fundamental group as well.

math.DG↗

arXiv2020

Obstructions to free actions on Bazaikin spaces

Apart from spheres and an infinite family of manifolds in dimension seven, Bazaikin spaces are the only known examples of simply connected Riemannian manifolds with positive sectional curvature in odd dimensions. We consider positively curved Riemannian manifolds whose universal covers have the same cohomology as Bazaikin spaces and prove structural results for the fundamental group in the presence of torus symmetry

math.DG↗