Phương trình đường trắc địa cực tiểu trên đa tạp với mật độ các đường trắc địa trên mặt phẳng với mật độ tuyến tính

Le Nam Tran1
1 Dong Thap University

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Abstract

The article generalizes the notion of geodesic curves in manifolds with density and presents their equations based on Christoffel symbols. Accordingly, we prove that on plane with linear density, of all curves joining the two points of p and q, the curve  minimizes density arc-length if and only if its curvature equals 0.

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References

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