Abstract
In this paper we define nth order Hessian structures on manifolds and study them. In particular, whenn = 3, we make a detailed study and establish a one-to-one correspondence betweenthird-order Hessian structures and acertain class of connections on the second-order tangent bundle of a manifold. Further, we show that a connection on the tangent bundle of a manifold induces a connection on the second-order tangent bundle. Also we define second-order geodesics of special second-order connection which gives a geometric characterization of symmetric third-order Hessian structures.
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David Kumar, R. Higher order Hessian structures on manifolds. Proc Math Sci 115, 259–277 (2005). https://doi.org/10.1007/BF02829657
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DOI: https://doi.org/10.1007/BF02829657