3.30 pm,Seminar Hall,CMI
Curvature, torsion and the quadrilateral gaps
Nitin Nitsure
TIFR.
04-11-19

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Abstract

If we travel on a flat plane by going straight for a distance s, then turn left in 90 degrees and go straight for the same distance s, and then repeat the turn and the straight travel twice more, then we complete a square and come back where we started. But if we do this on a curved surface, we will not come back exactly: the quadrilateral will not close but will have a gap between the starting point and the end point. Rajaram Nityananda asked for a quantification of this gap when s is small, and its relationship with curvature. We will answer this question, and prove a general higher dimensional theorem that characterizes the torsion and curvature of an affine connection in terms of such quadrilateral gaps.

Reference: arXiv:1910.06615