Florin Belgun

Nearly Kähler 6-Manifolds with Reduced Holonomy

We consider a complete six-dimensional nearly Kählermanifold together with the first canonical Hermitian connection. We showthat if the holonomy of this connection is reducible, then the manifoldendowed with a modified metric and almost complex structure is aKählerian twistor space. This result was conjectured byReyes-Carrión.

Killing Forms on Symmetric Spaces

Abstract Killing forms on Riemannian manifolds are differential forms whose covariant derivative is totally skew-symmetric. We show that a compact simply connected symmetric space carries a non-parallel Killing p-form ( p ⩾ 2 ) if and only if it isometric to a Riemannian product S k × N , where S k is a round sphere and k > p .

Symmetries of Contact Metric Manifolds

We study the Lie algebra of infinitesimal isometries on compact Sasakian and K-contact manifolds. On a Sasakian manifold which is not a space form or 3-Sasakian, every Killing vector field is an infinitesimal automorphism of the Sasakian structure. For a manifold with K-contact structure, we prove that there exists a Killing vector field of constant length which is not an infinitesimal automorphism of the structure if and only if the manifold is obtained from the Konishi bundle of a compact pseudo-Riemannian quaternion-Kähler manifold after changing the sign of the metric on a maximal negative distribution. We also prove that nonregular Sasakian manifolds are not homogeneous and construct examples with cohomogeneity one. Using these results we obtain in the last section the classification of all homogeneous Sasakian manifolds.

ESSENTIAL POINTS OF CONFORMAL VECTOR FIELDS

An essential point of a conformal vector fieldon a conformal manifold (M,c) is a point around which the local flow ofpreserves no metric in the conformal class c. It is well-known that a conformal vector field vanishes at each essential point. In this note we show that essential points are isolated. This is a generalization to higher dimensions of the fact that the zeros of a holomorphic function are isolated. As an application, we show that every connected component of the zero set of a conformal vector field is totally umbilical.

On the irreducibility of locally metric connections

A locally metric connection on a smooth manifold

The Einstein–Dirac equation on Sasakian 3-manifolds ☆

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On the boundary behavior of left-invariant Hitchin and hypo flows

is a torsion-free connection

On the Weyl tensor of a self-dual complex 4-manifold

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Locally conformally symplectic convexity

on

Geodesics and submanifold structures in conformal geometry

TM