Turkish Journal of Mathematics
Abstract
Given a closed 3-manifold $M^3$ endowed with a radial symmetric metric of negative sectional curvature, we define the cross curvature flow on $M^3$; using the maximum principle theorem, we demonstrated that the solution to the cross curvature flow exists for all time and converges pointwise to a hyperbolic metric.
DOI
10.3906/mat-1812-90
Keywords
Cross curvature flow, geometric evolution equation, negative sectional curvature
First Page
2444
Last Page
2450
Recommended Citation
LIAO, W (2019). The eternal solution to the cross curvature flow exists in 3-manifolds of negative sectional curvature. Turkish Journal of Mathematics 43 (5): 2444-2450. https://doi.org/10.3906/mat-1812-90
