Proceedings Mathematical Sciences

, Volume 115, Issue 3, pp 259–277 | Cite as

Higher order Hessian structures on manifolds

  • R. David Kumar


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.


Hessian structure connection geodesic 


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Copyright information

© Indian Academy of Sciences 2005

Authors and Affiliations

  • R. David Kumar
    • 1
  1. 1.Department of Collegiate EducationGovernment of Andhra PradeshHyderabadIndia

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