 
Summary: DOI: 10.1007/s002220040424x
Invent. math. 161, 151176 (2005)
On the stability of Riemannian manifold with parallel
spinors
Xianzhe Dai1
, Xiaodong Wang2,
, Guofang Wei1,
1 Department of Mathematics, UCSB, Santa Barbara, CA 93106, USA
(email: dai@math.ucsb.edu/wei@math.ucsb.edu)
2 Department of Mathematics, MIT, Cambridge, MA 02139, USA
(email: xwang@math.mit.edu)
Oblatum 10XI2003 & 4XI2004
Published online: 1 March 2005 SpringerVerlag 2005
Dedicated to Jeff Cheeger for his sixtieth birthday
Abstract. Inspired by the recent work [HHM03], we prove two stability
results for compact Riemannian manifolds with nonzero parallel spinors.
Our first result says that Ricci flat metrics which also admit nonzero parallel
spinors are stable (in the direction of changes in conformal structures) as
the critical points of the total scalar curvature functional. Our second result,
which is a local version of the first one, shows that any metric of positive
