Rotary Diffeomorphism onto Manifolds with Affine Connection

Abstract

In this paper we will introduce a newly found knowledge above the existence and the uniqueness of isoperimetric extremals of rotation on two-dimensional (pseudo-)Riemannian manifolds and on surfaces on Euclidean space. We will obtain the fundamental equations of rotary diffeomorphisms from (pseudo-)Riemannian manifolds for twice-differentiable metric tensors onto manifolds with affine connections.