Higher order Hessian structures on manifolds
- 49 Downloads
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.
KeywordsHessian structure connection geodesic
Unable to display preview. Download preview PDF.
- Ambrose W, Palais R S and Singer I M, Sprays (Anais da Academia Brasileira de Ciencias) (1960) vol. 32Google Scholar
- David Kumar R, Second and higher order structures on manifolds, Ph.D. thesis (Hyderabad, India: University of Hyderabad) (1995) (unpublished)Google Scholar
- Fomin V E, Differential geometry of Banach manifolds, Russian version (Publishing House of Kazan University) (1983)Google Scholar
- Flaschel P and Klingenberg W, Riemannsche Hilbert-mannigfalting keiten. Periodische Geodatische, LNM 282 (Berlin-Heidelberg, New York: Springer-Verlag) (1972)Google Scholar
- Juhani Fiskaali, Sauli Luukkonen and Eljas Maatta, On the differential geometry of bounded projections on Banach spaces, Preprint (July, 1987)Google Scholar
- Libermann P and Charles Michael Marle, Sympletic geometry and analytical mechanics (Dordrecht, Holland: D. Reidel Publishing Company) (1987)Google Scholar
- Nelson E, Topics in dynamics I: Flows, Preliminary Informal Notes of University Courses and Seminars in Mathematics. Mathematical Notes (Princeton: Princeton University Press and the University of Tokyo Press) (1969)Google Scholar
- Nickerson H K, Spencer D C and Steenrod N E, Advanced Calculus (London: D. Van Nostrand Company Inc.) (1959)Google Scholar
- Spivak Michael, A comprehensive introduction to differential geometry, second edition (Houston, Texas: Publish or Perish Inc.) (1970) vol.II Google Scholar