| | |
Summary: Abstract of the Dissertation
Aspects of Positively Ricci Curved Spaces:
New Examples and the Fundamental Group
by
Guofang Wei
Doctor of Philosophy
in
Mathematics
State University of New York at Stony Brook
1989
For a simply connected nilpotent Lie group L, we construct a complete
metric with positive Ricci curvature on the product manifold L \Theta R p , where
p is taken sufficiently large. The construction uses a warped product method
and involves subtle choices of functions. We endow L with a family of al
most flat metrics, and the little ``negativeness'' of L can be compensated by
warping the euclidean R p factor. From the construction one also sees that
the isometry group of the resulting manifold contains the original group L.
iii
A basic consequence of this construction is that every finitely generated
|
