Geodesic Sandwich Theorem with an Application

2018/06/19 by Shaikh, Absos Ali, Agarwal, Ravi P., Mondal, Chandan Kumar
#26B25 #39B62 #52A20 #52A30 #52A41 #53C22 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.07219

Abstract

The main goal of the paper is to prove the sandwich theorem for geodesic convex functions in a complete Riemannian manifold. Then by using this theorem we have proved an inequality in a manifold with bounded sectional curvature. Finally, we have shown that the gradient of a convex function is orthogonal to the tangent vector at some point of any geodesic.

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