On the existence of balanced metrics on six-manifolds of cohomogeneity one

We consider balanced metrics on complex manifolds with holomorphically trivial canonical bundle, most commonly known as balanced SU(n)-structures. Such structures are of interest for both Hermitian geometry and string theory, since they provide the ideal setting for the Hull–Strominger system. In this paper, we provide a non-existence result for balanced non-Kähler $$\text {SU}(3)$$ SU ( 3 ) -structures which are invariant under a cohomogeneity one action on simply connected six-manifolds.

Complex Spacetimes and the Newman-Janis Trick

<p>In this thesis, we explore the subject of complex spacetimes, in which the mathematical theory of complex manifolds gets modified for application to General Relativity. We will also explore the mysterious Newman-Janis trick, which is an elementary and quite short method to obtain the Kerr black hole from the Schwarzschild black hole through the use of complex variables. This exposition will cover variations of the Newman-Janis trick, partial explanations, as well as original contributions.</p>

Complex Spacetimes and the Newman-Janis Trick

<p>In this thesis, we explore the subject of complex spacetimes, in which the mathematical theory of complex manifolds gets modified for application to General Relativity. We will also explore the mysterious Newman-Janis trick, which is an elementary and quite short method to obtain the Kerr black hole from the Schwarzschild black hole through the use of complex variables. This exposition will cover variations of the Newman-Janis trick, partial explanations, as well as original contributions.</p>

Dolbeault and J-Invariant Cohomologies on Almost Complex Manifolds

In this paper we relate the cohomology of J-invariant forms to the Dolbeault cohomology of an almost complex manifold. We find necessary and sufficient condition for the inclusion of the former into the latter to be true up to isomorphism. We also extend some results obtained by J. Cirici and S. O. Wilson about the computation of the left-invariant cohomology of nilmanifolds to the setting of solvmanifolds. Several examples are given.