Differential geometry of higher order
نویسندگان
چکیده
منابع مشابه
Noncommutative Differential Geometry with Higher Order Derivatives
We build a toy model of differential geometry on the real line, which includes derivatives of the second order. Such construction is possible only within the framework of noncommutative geometry. We introduce the metric and briefly discuss two simple physical models of scalar field theory and gauge theory in this geometry. TPJU 2/94 January 1994 Partially supported by KBN grant 2 P302 168 4 E-m...
متن کاملRecurrent metrics in the geometry of second order differential equations
Given a pair (semispray $S$, metric $g$) on a tangent bundle, the family of nonlinear connections $N$ such that $g$ is recurrent with respect to $(S, N)$ with a fixed recurrent factor is determined by using the Obata tensors. In particular, we obtain a characterization for a pair $(N, g)$ to be recurrent as well as for the triple $(S, stackrel{c}{N}, g)$ where $stackrel{c}{N}$ is the canonical ...
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In our previous papers (Nishimura [2001 and 2003]) we dealt with jet bundles from a synthetic perch by regarding a 1-jet as something like a pinpointed (nonlinear) connection (called a preconnection) and then looking on higherorder jets as repeated 1-jets. In this paper we generalize our notion of preconnection to higher orders, which enables us to develop a non-repetitive but still synthetic a...
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given a pair (semispray $s$, metric $g$) on a tangent bundle, the family of nonlinear connections $n$ such that $g$ is recurrent with respect to $(s, n)$ with a fixed recurrent factor is determined by using the obata tensors. in particular, we obtain a characterization for a pair $(n, g)$ to be recurrent as well as for the triple $(s, stackrel{c}{n}, g)$ where $stackrel{c}{n}$ is the canonical ...
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Krasnoselskii’s fixed-point theorem in a cone is used to discuss the existence of positive solutions to semipositone conjugate and (n, p) problems. @ 2004 Elsevier Ltd. All rights reserved. Keywords-Existence, Positive solution, Semipositone, Conjugate and (n,p) problems.
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ژورنال
عنوان ژورنال: Topology
سال: 1962
ISSN: 0040-9383
DOI: 10.1016/0040-9383(62)90103-9