Tight Lagrangian homology spheres in compact homogeneous Kähler manifolds
For any irreducible compact homogeneous Kähler manifold, we classify the compact tight Lagrangian submanifolds which have the Z_2-homology of a sphere.
math.DG↗
arXiv subjects
Fabio Podestà
Publications and source records attributed to Fabio Podestà.
Homogeneous Hypercomplex Structures and the Joyce's Construction
We prove that any invariant hypercomplex structure on a homogeneous space $M = G/L$ where $G$ is a compact Lie group is obtained via the Joyce's construction, provided that there exists a hyper-Hermitian naturally reductive invariant metric on $M$.
math.DG↗
Homogeneous Lagrangian submanifolds of positive Euler characteristic
We fully classify all Lagrangian submanifolds of a complex Grassmannian which are an orbit of a compact group of isometries and have positive Euler characteristic.
math.DG↗
Maximal totally complex submanifolds of $\mathbb{H}\mathbb{P}^n$: homogeneity and normal holonomy
We prove that a maximal totally complex submanifold $N^{2n}$ of the quaternionic projective space $\mathbb{H}\mathbb{P}^n$ ($n\geq 2$) is a parallel submanifold, provided one of the following conditions is satisfied: (1) $N$ is the orbit of a compact Lie group of isometries, (2) the restricted normal holonomy is a proper subgroup of ${\rm U}(n)$.
math.DG↗
Polar and coisotropic actions on Kaehler manifolds
The main result of this paper is that a polar action on a compact irreducible homogeneous Kaehler manifold is coisotropic. This is then used to give new examples of polar actions and to classify coisotropic and polar actions on quadrics.
math.DG↗