 
Summary: Digital Object Identifier (DOI) 10.1007/s0022000309862
Commun. Math. Phys. 244, 335345 (2004) Communications in
Mathematical
Physics
A Positive Mass Theorem for Spaces
with Asymptotic SUSY Compactification
Xianzhe Dai
Department of Mathematics, University of California, Santa Barbara, CA 93106, USA.
Email: dai@math.ucsb.edu
Received: 16 June 2003 / Accepted: 8 August 2003
Published online: 25 November 2003 © SpringerVerlag 2003
Abstract: We prove a positive mass theorem for spaces which asymptotically approach
a flat Euclidean space times a CalabiYau manifold (or any special honolomy manifold
except the quaternionic Kšahler). This is motivated by the very recent work of Hertog
HorowitzMaeda [HHM].
In general relativity, isolated gravitational systems are modelled by asymptotically flat
spacetimes. The spatial slices of such spacetime are then asymptotically flat Riemannian
manifolds. That is, Riemannian manifolds (Mn, g) such that M = M0 M with M0
compact and M Rn
 BR(0) for some R > 0 so that in the induced Euclidean
