We continue the investigation of Spin(7) holonomy metric of cohomogeneity one with the principal orbit SU(3)/U(1). A special choice of U(1) embedding in SU(3) allows more general metric ansatz with five metric functions. There are two possible singular orbits in the first order system of Spin(7) instanton equation. One is the flag manifold SU(3)/T 2 also known as the twister space of CP(2) and ...

We construct explicit cohomogeneity two metrics of G 2 holonomy, which are foliated by twistor spaces. The twistor spaces are S 2 bundles over four-dimensional Bianchi IX Einstein metrics with self-dual (or anti-self-dual) Weyl tensor. Generically the 4-metric is of triaxial Bianchi IX type, with SU (2) isometry. We derive the first-order differential equations for the metric coefficients, and ...

We construct infinitely many new 1-parameter families of simply connected complete non-compact G$\_2$-manifolds with controlled geometry at infinity. The generic member each family has so-called asymptotically locally conical (ALC) geometry. However, the nature asymptotic changes two special parameter values: one value we obtain a unique (AC) geometry; on approach to other metrics collapses an ...

In this paper, we look for metrics of cohomogeneity one in D = 8 and D = 7 dimensions with Spin(7) and G 2 holonomy respectively. In D = 8, we first consider the case of principal orbits that are S 7 , viewed as an S 3 bundle over S 4 with triaxial squashing of the S 3 fibres. This gives a more general system of first-order equations for Spin(7) holonomy than has been solved previously. Using n...

Abstract The symmetrized bidisc $$\begin{aligned} G {\mathop {=}\limits ^\mathrm{{def}}}\{(z+w,zw):|z|&lt;1,\quad |w|&lt;1\}, \end{aligned}$$ G = def { ( z +</m...

As a means to better understanding manifolds with positive curvature, there has been much recent interest in the study of nonnegatively curved manifolds which contain a point at which all 2-planes have positive curvature. We show that there are generalisations of the well-known Eschenburg spaces together with quotients of S×S which admit metrics with this property. It is an unfortunate fact tha...

An important question in the study of Riemannian manifolds of positive sectional curvature is how to distinguish manifolds that admit a metric with non-negative sectional curvature from those that admit one of positive curvature. Surprisingly, if the manifolds are compact and simply connected, all known obstructions to positive curvature are already obstructions to non-negative curvature. On th...

In this paper we prove the existence of Einstein metrics, actually SasakianEinstein metrics, on nontrivial rational homology spheres in all odd dimensions greater than 3. It appears as though little is known about the existence of Einstein metrics on rational homology spheres, and the known ones are typically homogeneous. The are two exception known to the authors. Both involve Sasakian geometr...

Nov.11th (FRI), 11:00–12:00 •H. Tsuji (Sophia University) “Variation of Bergman Kernels and its applications” We prove semipositivity of the curvature of the Narashimhan-Simha metric on an arbitrary flat projective family of varieties with only canonical singularities. This method gives a simple analytic proof and a generalization of Viehweg’s result which proves the quasiprojectivity of the mo...