Turkish Journal of Mathematics
DOI
-
Abstract
We consider the cross curvature flow, an evolution equation of metrics on 3-manifolds. We establish short time existence when the sectional curvature has a sign. In the case of negative sectional curvature, we obtain some monotonicity formulas which support the conjecture that after normalization, for initial metrics on closed 3-manifolds with negative sectional curvature, the solution exists for all time and converges to a hyperbolic metric. This conjecture is still open at the present time.
Keywords
Cross curvature flow, geometric evolution equation, negative sectional curvature, monotonicity formula, hyperbolic metric
First Page
1
Last Page
10
Recommended Citation
CHOW, BENNETT and HAMILTON, RICHARD S. (2004) "The Cross Curvature Flow of 3-Manifolds with Negative Sectional Curvature," Turkish Journal of Mathematics: Vol. 28: No. 1, Article 1. Available at: https://journals.tubitak.gov.tr/math/vol28/iss1/1
