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JP Journal of Geometry and Topology
JP Journal of Geometry and Topology
Volume 6, Issue 3, Pages 303 - 318 (November 2006)
SPACE-TIME FORMULATION FOR CURVATURE FLOW OF HIGH CODIMENSION
Guanghan Li (Portugal and P. R. China) and Isabel M. C. Salavessa (Portugal)
Abstract
We consider the motion of submanifolds in a Riemannian manifold in the direction of one normal vector. As in the case of hypersurfaces, we define the Harnack quantity of this flow and an affine second fundamental form with respect to a degenerate metric on the space-time track of the submanifold. Then we show that this Harnack quantity is corresponding to the affine second fundamental form of the space-time track.
Keywords and phrases:
Harnack quantity, space-time track, affine second fundamental form, curvature flow.
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ISSN: 0972-415X
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