Mihaela Pilca

Higher rank homogeneous Clifford structures

We give an upper bound for the rank r of homogeneous (even) Clifford structures on compact manifolds of non-vanishing Euler characteristic. More precisely, we show that if r = 2 a · b with b odd, then r ≤ 9 for a = 0, r ≤ 10 for a = 1, r ≤ 12 for a = 2 and r ≤ 16 for a ≥ 3. Moreover, we describe the four limiting cases and show that there is exactly one solution in each case.

Kählerian twistor spinors

On a Kähler spin manifold, Kählerian twistor spinors are a natural analogue of twistor spinors on Riemannian spin manifolds. They are defined as sections in the kernel of a first order differential operator adapted to the Kähler structure, called Kählerian twistor (Penrose) operator. We study Kählerian twistor spinors and give a complete description of compact Kähler manifolds of constant scalar curvature admitting such spinors. As in the Riemannian case, the existence of Kählerian twistor spinors is related to the lower bound of the spectrum of the Dirac operator.

Toric Vaisman manifolds

Abstract Vaisman manifolds are strongly related to Kahler and Sasaki geometry. In this paper we introduce toric Vaisman structures and show that this relationship still holds in the toric context. It is known that the so-called minimal covering of a Vaisman manifold is the Riemannian cone over a Sasaki manifold. We show that if a complete Vaisman manifold is toric, then the associated Sasaki manifold is also toric. Conversely, a toric complete Sasaki manifold, whose Kahler cone is equipped with an appropriate compatible action, gives rise to a toric Vaisman manifold. In the special case of a strongly regular compact Vaisman manifold, we show that it is toric if and only if the corresponding Kahler quotient is toric.

On toric locally conformally Kähler manifolds

We study compact toric strict locally conformally Kähler manifolds. We show that the Kodaira dimension of the underlying complex manifold is

A NOTE ON THE CONFORMAL INVARIANCE OF G-GENERALIZED GRADIENTS

-\infty

Generalized Gradients of G-Structures and Kählerian Twistor Spinors

-∞, and that the only compact complex surfaces admitting toric strict locally conformally Kähler metrics are the diagonal Hopf surfaces. We also show that every toric Vaisman manifold has lcK rank 1 and is isomorphic to the mapping torus of an automorphism of a toric compact Sasakian manifold.

Conformally related K\"ahler metrics and the holonomy of lcK manifolds

An almost quaternion-Hermitian structure on a Riemannian manifold