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On an oriented surface, the integral of the Gauss curvature over a smooth triangle can be interpreted as the angle of rotation of a vector that is parallel translated once around the three bounding edges.
How does one interpret the integral of the Gauss curvature of an arbitrary SO(20 bundle with connection over a triangle on a surface?
Does this question have a different answer if the associated vector bundle has a compatible Riemannian metric?
Are there special SO(2) bundles - other than the tangent bundle - where the integral has special meaning? How about on higher dimensionl manifolds?
How does one interpret the integral of the Gauss curvature of an arbitrary SO(20 bundle with connection over a triangle on a surface?
Does this question have a different answer if the associated vector bundle has a compatible Riemannian metric?
Are there special SO(2) bundles - other than the tangent bundle - where the integral has special meaning? How about on higher dimensionl manifolds?
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