Compact Gradient Shrinking Ricci Solitons with Positive Curvature Operator

Details Compact Gradient Shrinking Ricci Solitons with Positive Curvature Operator Compact Gradient Shrinking Ricci Solitons with Positive Curvature Operator

2006-01-25

arxiv.org/abs/math/0601599v1

Mathematics

Differential Geometry

10 pages

Scientific paper

In this paper, we study the following conjecture of Hamilton: Any compact
gradient shrinking Ricci soliton with positive curvature operator must be
Einstein. We first derive several identities. Then we show that the conjecture
is true under an additional condition. Furthermore, such a soliton must be of
constant curvature.

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