A LOWER BOUND FOR TOTAL CURVATURE OF A CLOSED CURVE IN A CAT(K) SPACE
A lower bound for total curvature of a closed curve in a metric space of nonzero curvature in the sense of Alexandrov is investigated in this paper. We find that the total curvature of a closed curve is greater than in case of and is more than or equal to in case of where its perimeter Our results extend some well-known facts proved by Tsukamoto [18] and Teufel [16, 17].
total curvature, closed curve, CAT(K).