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Steady Ricci flows

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Abstract

Steady solutions for Ricci flows are given. A class of Riemannian 3-manifolds related to the geometry of a surface is considered. The components of the metric tensor, which reproduce the Riemannian space and a triorthogonal coordinate system, are determined by a system of partial differential equations. In the stationary case, the curvature tensor of the space satisfies six equations determining the metric of the space. The exact analytic solutions corresponding to surfaces of constant Gaussian and mean curvature (n = 3) are written. Arbitrary curvilinear coordinate systems are constructed, on which the construction of structured grids is based.

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Authors and Affiliations

  1. Institute of Computer-Aided Design, Russian Academy of Sciences, Vtoraya Brestskaya ul. 19/18, Moscow, 123056, Russia

    Yu. D. Shevelev

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  1. Yu. D. Shevelev
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Correspondence to Yu. D. Shevelev.

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Original Russian Text © Yu.D. Shevelev, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 1, pp. 26–28.

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Shevelev, Y.D. Steady Ricci flows. Dokl. Math. 92, 778–780 (2015). https://doi.org/10.1134/S1064562415060046

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