Higher order Hessian structures on manifolds

In this paper we define \(n\)th order Hessian structures on manifolds and study them. In particular, when \(n = 3\), we make a detailed study and establish a one-to-one correspondence between {\it third-order Hessian structures} and a {\it certain class of connections} on the second-order tangent bu...

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Bibliographic Details
Published inarXiv.org
Main Author Kumar, R David
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.08.2005
Subjects
Bundling
Geodesy
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Summary:In this paper we define \(n\)th order Hessian structures on manifolds and study them. In particular, when \(n = 3\), we make a detailed study and establish a one-to-one correspondence between {\it third-order Hessian structures} and a {\it certain 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.
ISSN:2331-8422