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- W2588513004 abstract "In this paper, we investigate the Gauss maps of a Ricci-mean curvature flow. A Ricci-mean curvature flow is a coupled equation of a mean curvature flow and a Ricci flow on the ambient manifold. Ruh and Vilms (Trans Am Math Soc 149: 569–573, 1970) proved that the Gauss map of a minimal submanifold in a Euclidean space is a harmonic map, and Wang (Math Res Lett 10(2–3):287–299, 2003) extended this result to a mean curvature flow in a Euclidean space by proving its Gauss maps satisfy the harmonic map heat flow equation. In this paper, we deduce the evolution equation for the Gauss maps of a Ricci-mean curvature flow, and as a direct corollary we prove that the Gauss maps of a Ricci-mean curvature flow satisfy the vertically harmonic map heat flow equation when the codimension of submanifolds is 1." @default.
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- W2588513004 date "2017-07-12" @default.
- W2588513004 modified "2023-10-17" @default.
- W2588513004 title "Gauss maps of the Ricci-mean curvature flow" @default.
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- W2588513004 doi "https://doi.org/10.1007/s10711-017-0271-8" @default.
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