The structure of compact Ricci-flat Riemannian manifolds

@article{Fischer1975TheSO,
  title={The structure of compact Ricci-flat Riemannian manifolds},
  author={Arthur Elliot Fischer and Joseph A. Wolf},
  journal={Journal of Differential Geometry},
  year={1975},
  volume={10},
  pages={277-288}
}
where k is the first Betti number b^M), T is a flat riemannian λ -torus, M~ is a compact connected Ricci-flat (n — λ;)-manifold, and Ψ is a finite group of fixed point free isometries of T x M' of a certain sort (Theorem 4.1). This extends Calabi's result on the structure of compact euclidean space forms ([7] see [20, p. 125]) from flat manifolds to Ricci-flat manifolds. We use it to essentially reduce the problem of the construction of all compact Ricci-flat riemannian ^-manifolds to the… 
The Calabi construction for compact Ricci flat Riemannian manifolds
1. The main result and some consequences. In 1956 E. Calabi [6] attacked the classification problem of compact euclidean space forms by means of a special construction, called the Calabi construction
Asymptotically cylindrical Calabi-Yau manifolds
Let M be a complete Ricci-flat Kahler manifold with one end and assume that this end converges at an exponential rate to [0,oo) x X for some compact connected Ricci-flat manifold X. We begin by
Holonomy rigidity for Ricci-flat metrics
On a closed connected oriented manifold M we study the space $$\mathcal {M}_\Vert (M)$$M‖(M) of all Riemannian metrics which admit a non-zero parallel spinor on the universal covering. Such metrics
Dominant energy condition and spinors on Lorentzian manifolds
Let (M, g) be a timeand space-oriented Lorentzian spin manifold, and let M be a compact spacelike hypersurface of M with induced Riemannian metric g and second fundamental form K. If (M, g) satisfies
Manifolds of Riemannian metrics with prescribed scalar curvature
THEOREM 2. Assume J * V 0 . Writing UtQ=(je a o\0 )U&9 J(\ is the disjoint union of closed submanifolds. REMARK. If d i m M = 2 , e^J=^" 8 , and if d i m M = 3 , the hypothesis that 1F*J£0 can be
Contributions to the geometry of Lorentzian manifolds with special holonomy
In the present thesis we study (n+ 2)-dimensional Lorentzian manifolds (M(n+2), g) with special holonomy, i.e. such that their holonomy representation acts indecomposably but non-irreducibly. Being
Heterotic solitons on four-manifolds
We investigate four-dimensional Heterotic solitons, defined as a particular class of solutions of the equations of motion of Heterotic supergravity on a four-manifold M . Heterotic solitons depend on
Supersymmetry, Ricci flat manifolds and the String Landscape
  • B. Acharya
  • Mathematics
    Journal of High Energy Physics
  • 2020
Abstract A longstanding question in superstring/M theory is does it predict supersymmetry below the string scale? We formulate and discuss a necessary condition for this to be true; this is the
On Riemann-Roch Formula, Chern Numbers and the Betti Numbers of Irreducible Compact Hyperkähler Manifolds—n = 4
The study of higher dimensional hyperkähler manifolds caught much attentions (to save our space, we only mention some of them), we have [Wk], [Bg1,2,3,4], [Fj1,2], [Bv1], [OG1,2], [Vb1,2], [Sl1,2],
...
...

References

SHOWING 1-10 OF 28 REFERENCES
Manifolds of Riemannian metrics with prescribed scalar curvature
THEOREM 2. Assume J * V 0 . Writing UtQ=(je a o\0 )U&9 J(\ is the disjoint union of closed submanifolds. REMARK. If d i m M = 2 , e^J=^" 8 , and if d i m M = 3 , the hypothesis that 1F*J£0 can be
Vector fields and Ricci curvature
We shall prove theorems on nonexistence of certain types of vector fields on a compact manifold with a positive definite Riemannian metric whose Ricci curvature is either everywhere positive or
Growth of finitely generated solvable groups and curvature of Riemannian manifolds
If a group Γ is generated by a finite subset 5, then one has the "growth function" gs, where gs(m) is the number of distinct elements of Γ expressible as words of length <m on 5. Roughly speaking, J.
The homology of Kummer manifolds
The theory of Kummer surfaces is a classical topic in algebraic geometry.1 A generalization to higher dimensions has been given by W. Wirtinger.2 The varieties introduced by Wirtinger may be called
Linearization stability of nonlinear partial differential equations
In this article we study solutions to systems of nonlinear partial differential equations that arise in riemannian geometry and in general relativity. The systems we shall be considering are the
Curvature and Betti numbers
*Frontmatter, pg. i*Preface, pg. v*Contents, pg. vii*Chapter I. Riemannian Manifold, pg. 2*Chapter II. Harmonic and Killing Vectors, pg. 26*Chapter III. Harmonic and Killing Tensors, pg. 59*Chapter
What is tensor analysis?
TLDR
Doctor Banesh Hoffmann’s article is the best elementary analysis of the subject which I have seen.
...
...