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2D RICCI FLAT GRADIENT SOLITONS ARISING FROM REMARKABLE MODELS IN PHYSICS
, 2013On a pseudo-Riemannian manifold (M, g) we consider ∇ the Levi-Civita connection associated to metric g and a function f : M → ℝ whose pseudo-Riemannian Hessian is non-degenerate and with constant signature.
G. Bercu
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SUPERCONFORMAL SYMMETRY AND GEOMETRY OF RICCI-FLAT KÄHLER MANIFOLDS
International Journal of Modern Physics A, 1989A supersymmetric nonlinear σ-model provides us a tool for studying the dynamics of superstrings on a compactified space. If the compactified space is a Ricci-flat Kähler manifold, the nonlinear σ-model has extended superconformal symmetry and the partition function of the model is expressed in terms of characters of the superconformal algebra.
Hirosi Ooguri, Hirosi Ooguri
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Classification of the static vacuum metric with Ricci-flat compactification.
Physical Review D, Particles and fields, 1986We explicitly construct all spherically symmetric vacuum solutions of the higher-dimensional Einstein equation in which the size of Ricci-flat compact internal manifolds varies with three-dimensional distance, subject to an asymptotic condition, flat M ...
Yoshimura
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Spontaneous compactification and Ricci-flat manifolds with torsion
Journal of Mathematical Physics, 1986The Freund–Rubin mechanism is based on the equation Rik=λgik (where λ>0), which, via Myers’ theorem, implies ‘‘spontaneous’’ compactification. The difficulties connected with the cosmological constant in this approach can be resolved if torsion is introduced and λ is set equal to zero, but then compactification ‘‘by hand’’ is necessary since the
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Asymptotically Euclidean Ends of Ricci Flat Manifolds, and Conformal Inversions
Mathematische Nachrichten, 2000We prove that a Ricci flat end of a Riemannian manifold is asymptotically Euclidean if it is obtained from a smooth metric by a conformal inversion. A number of consequences are discussed.
Hans-Bert Rademacher, Wolfgang Kühnel
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Gravitational Instantons and Degenerations of Ricci-flat Metrics on the K3 Surface
, 2020Lorenzo Foscolo
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Holomorphic deformations of the Ricci-flat $$\partial \overline \partial $$ -manifolds
Acta Mathematica Sinica, English Series, 2016We present a construction of globally convergent power series of integrable Beltrami differentials on the Ricci-flat $$\partial \overline \partial $$ -manifolds and also a construction of global canonical family of holomorphic (n, 0)-forms on the deformation ...
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