Add to ORKGAbstract. In the classification of Riemannian holonomy groups, the exceptional holonomy groups are G2 in 7 dimensions, and Spin(7) in 8 dimensions. We outline the construction of the first known examples of compact 7- and 8-manifolds with holonomy G2 and Spin(7). In the case of G2, we first choose a finite group Γ of automorphisms of the torus T 7 and a flat Γ-invariant G2-structure on T 7, so that T 7/Γ is an orbifold. Then we resolve the singularities of T 7/Γ to get a compact 7-manifold M. Finally we use analysis, and an understanding of Calabi-Yau metrics, to construct a family of metrics with holonomy G2 on M, which converge to the singular metric on T 7/Γ
A G2-manifold is a Riemannian manifold whose holonomy group is contained in the exceptional Lie grou...
$G_2$-structures defined by a closed positive 3-form constitute the starting point in known and pote...
The work in this thesis is an investigation of the geometric structures arising on S 1 and T 2 q...
The exceptional holonomy groups are G2 in 7 dimensions, and Spin(7) in 8 dimensions. Riemannian mani...
The exceptional holonomy groups are G2 in 7 dimensions, and Spin(7) in 8 dimensions. In a previous p...
The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, ...
The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, ...
Compact Riemannian 7- and 8-manifolds with holonomy G(2) arid Spin(7) were first constructed by the ...
Compact Riemannian 7- and 8-manifolds with holonomy G(2) arid Spin(7) were first constructed by the ...
Suppose that M is an orientable n-dimensional manifold, and g a Riemannian metric on M. Then the hol...
This is the second of two papers about metrics of holonomy G2 on compact 7-manifolds. In our first p...
In Berger's classification of Riemannian holonomy groups there are several infinite families and two...
We use classical obstruction theory \`{a} la Eilenberg-Steenrod to obtain a homotopy classification ...
We use classical obstruction theory \`{a} la Eilenberg-Steenrod to obtain a homotopy classification ...
In Berger's classification of Riemannian holonomy groups there are several infinite families and tw...
A G2-manifold is a Riemannian manifold whose holonomy group is contained in the exceptional Lie grou...
$G_2$-structures defined by a closed positive 3-form constitute the starting point in known and pote...
The work in this thesis is an investigation of the geometric structures arising on S 1 and T 2 q...
The exceptional holonomy groups are G2 in 7 dimensions, and Spin(7) in 8 dimensions. Riemannian mani...
The exceptional holonomy groups are G2 in 7 dimensions, and Spin(7) in 8 dimensions. In a previous p...
The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, ...
The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, ...
Compact Riemannian 7- and 8-manifolds with holonomy G(2) arid Spin(7) were first constructed by the ...
Compact Riemannian 7- and 8-manifolds with holonomy G(2) arid Spin(7) were first constructed by the ...
Suppose that M is an orientable n-dimensional manifold, and g a Riemannian metric on M. Then the hol...
This is the second of two papers about metrics of holonomy G2 on compact 7-manifolds. In our first p...
In Berger's classification of Riemannian holonomy groups there are several infinite families and two...
We use classical obstruction theory \`{a} la Eilenberg-Steenrod to obtain a homotopy classification ...
We use classical obstruction theory \`{a} la Eilenberg-Steenrod to obtain a homotopy classification ...
In Berger's classification of Riemannian holonomy groups there are several infinite families and tw...
A G2-manifold is a Riemannian manifold whose holonomy group is contained in the exceptional Lie grou...
$G_2$-structures defined by a closed positive 3-form constitute the starting point in known and pote...
The work in this thesis is an investigation of the geometric structures arising on S 1 and T 2 q...