Publications

1997

• Parallel and Killing Spinors on Spin^c Manifolds
  
  • Moroianu Andrei
  Communications in Mathematical Physics, Springer Verlag, 1997, 187, pp.417-427. We describe all simply connected Spin^c manifolds carrying parallel and real Killing spinors. In particular we show that every Sasakian manifold (not necessarily Einstein) carries a canonical Spin^c structure with Killing spinors. (10.1007/s002200050142)
  DOI : 10.1007/s002200050142
• On Kirchberg's Inequality for Compact Kähler Manifolds of Even Complex Dimension
  
  • Moroianu Andrei
  Annals of Global Analysis and Geometry, Springer Verlag, 1997, 15, pp.235-242. In 1986 Kirchberg showed that each eigenvalue of the Dirac operator on a compact Kähler manifold of even complex dimension satisfies some inequality involving the scalar curvature. It is conjectured that the manifolds for the limiting case of this inequality are products T^2×N, where T^2 is a flat torus and N is the twistor space of a quaternionic Kähler manifold of positive scalar curvature. In 1990 Lichnerowicz announced an affirmative answer for this conjecture, but his proof seems to work only when assuming that the Ricci tensor is parallel. The aim of this note is to prove several results about manifolds satisfying the limiting case of Kirchberg''s inequality and to prove the above conjecture in some particular cases. (10.1023/A:1006543304443)
  DOI : 10.1023/A:1006543304443
• On nearly parallel G_2-structures
  
  • Friedrich Thomas
  • Kath Ines
  • Moroianu Andrei
  • Semmelmann Uwe
  Journal of Geometry and Physics, Elsevier, 1997, 23, pp.259-286. A nearly parallel G_2-structure on a seven-dimensional Riemannian manifold is equivalent to a spin structure with a Killing spinor. We prove general results about the automorphism group of such structures and we construct new examples. We classify all nearly parallel G_2-manifolds with large symmetry group and in particular all homogeneous nearly parallel G_2-structures. (10.1016/S0393-0440(97)80004-6)
  DOI : 10.1016/S0393-0440(97)80004-6
• Boundary effect for an elliptic Neumann problem with critical nonlinearity
  
  • Rey Olivier
  Communications in Partial Differential Equations, Taylor & Francis, 1997, 22 (7-8), pp.1055-1139. We are interested in elliptic problems with critical nonlinearity and Neumann boundary conditions, namely (P_μ) : -Δu + μu = u^(n+2)/(n-2), u>0 in Ω, ∂u/∂ν = 0 on ∂Ω — where Ω is a smooth bounded domain in ℝ^n, n≥3, and μ is a strictly positive parameter. We show, for n≥7, and u a small energy solution to (P_μ), that u concentrates as μ goes to infinity at a point of the boundary such that the mean curvature H is positive, and critical if it is strictly positive. Conversely we show, for n≥5, and α>0 a critical value of H inducing a difference of topology between the level sets of H, that there exists for μ large enough a solution to (P_μ) which concentrates at a point y of the boundary such that H(y) = α and H'(y) = 0. Lastly, if n≥6 and y_1, … , y_k are k distinct critical points of H, there exists for μ large enough a solution to (P_μ) which concentrates at each of the points y_i, 1≤i≤k.