N. I. Manina, A. Ya. Sultanov, “Infinitesimal affine transformations of the second order tangent bundle with horizontal lift connection”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, Number 9,Pages <nobr>62

This article is cited in 2 papers

Infinitesimal affine transformations of the second order tangent bundle with horizontal lift connection

N. I. Manina^a, A. Ya. Sultanov^b

^a Scientific and Technical Enterprise "Cryptosoft", Penza, Russia
^b Chair of Algebra, Penza State Pedagogical University, Penza, Russia

Abstract: We obtain the canonical expansion of an infinitesimal affine transformation of the second order tangent bundle with horizontal lift connection. We establish necessary and sufficient conditions under which a vector field is an infinitesimal affine transformation. We also construct the horizontal lift of a linear connection to a second orderWeil bundle.

Keywords: second order tangent bundle, linear connection, horizontal lift of a linear connection, infinitesimal affine transformation, second order Weil bundle.

UDC: 514.76

Received: 07.07.2010