scholarly journals Boundaries of zero scalar curvature in the $\mathrm{AdS}$/$\mathrm{CFT}$ correspondence

1999 ◽  
Vol 3 (6) ◽  
pp. 1769-1783 ◽  
Author(s):  
Mingliang Cai ◽  
Gregory J. Galloway
Keyword(s):  
Scalar Curvature ◽  
Zero Scalar Curvature

Two-ended hypersurfaces with zero scalar curvature

1999 ◽  
Vol 48 (3) ◽  
pp. 0-0 ◽  
Author(s):  
Jorge Hounie ◽  
Maria Luiza Leite
Keyword(s):  
Scalar Curvature ◽  
Zero Scalar Curvature

scholarly journals QUATERNIONIC CONNECTIONS, INDUCED HOLOMORPHIC STRUCTURES AND A VANISHING THEOREM

2008 ◽  
Vol 19 (10) ◽  
pp. 1167-1185 ◽  
Author(s):  
LIANA DAVID
Keyword(s):  
Scalar Curvature ◽  
Vanishing Theorem ◽  
Penrose Transform ◽  
Holomorphic Sections ◽  
Quaternionic Manifold ◽  
Structure Formula ◽  
Zero Scalar Curvature ◽  
Twistor Fibration ◽  
Tensor Powers ◽  
Quaternionic Kähler

We classify the holomorphic structures of the tangent vertical bundle Θ of the twistor fibration of a quaternionic manifold (M, Q) of dimension 4n ≥ 8. In particular, we show that any self-dual quaternionic connection D of (M, Q) induces an holomorphic structure [Formula: see text] on Θ. We construct a Penrose transform which identifies solutions of the Penrose operator PD on (M, Q) defined by D with the space of [Formula: see text]-holomorphic purely imaginary sections of Θ. We prove that the tensor powers Θs (for any s ∈ ℕ\{0}) have no global non-trivial [Formula: see text]-holomorphic sections, when (M, Q) is compact and has a compatible quaternionic-Kähler metric of negative (respectively, zero) scalar curvature and the quaternionic connection D is closed (respectively, closed but not exact).

On Stability of Cones in Rn+1 with Zero Scalar Curvature

2005 ◽  
Vol 28 (2) ◽  
pp. 107-122 ◽  
Author(s):  
J. L. M. Barbosa ◽  
M. P. Do Carmo
Keyword(s):  
Scalar Curvature ◽  
Zero Scalar Curvature
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