Mustafa Kalafat

Algebraic topology of G2 manifolds

Abstract In this paper we give a survey of various results about the topology of oriented Grassmannian bundles related to the exceptional Lie group G 2 . Some of these results are new. We give self-contained proofs here. One often encounters these spaces when studying submanifolds of manifolds with calibrated geometries. For the sake of completeness we decided to collect them here in a self-contained way to be easily accessible for future usage in calibrated geometry. As an application we deduce existence of certain special 3 and 4 dimensional submanifolds of G 2 manifolds with special properties, which appear in the first named author’s work with S. Salur about G 2 dualities.

Conformally Kähler surfaces and orthogonal holomorphic bisectional curvature

We show that a compact complex surface which admits a conformally Kähler metric

Geometric invariant theory and Einstein–Weyl geometry

g

On the curvature of Einstein-Hermitian Surfaces

g of positive orthogonal holomorphic bisectional curvature is biholomorphic to the complex projective plane. In addition, if

Locally conformally flat metrics on surfaces of general type.

g

On special submanifolds of the Page space

g is a Hermitian metric which is Einstein, then the biholomorphism can be chosen to be an isometry via which