Second-order structures on Banach manifolds

Abstract

Ambrose et al. (Sprays, Anais da Academia Brasileira de Ciencias, 32, 1-15 (1960)) introduced the concept of certain second-order structures on finite-dimensional manifolds, viz. dissection, Hessian structure and spray, and have shown that each of these structures uniquely determines and is determined by a symmetric connection. In this paper we extend these results to Banach manifolds. We define a Christoffel structure which is central to our
exposition and yields all the results.