Turkish Journal of Mathematics
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.
DOI
-
Keywords
Cross curvature flow, geometric evolution equation, negative sectional curvature, monotonicity formula, hyperbolic metric
First Page
1
Last Page
10
Recommended Citation
CHOW, B, & HAMILTON, R. S (2004). The Cross Curvature Flow of 3-Manifolds with Negative Sectional Curvature. Turkish Journal of Mathematics 28 (1): 1-10. https://doi.org/-
