Higher-Order Curvature and Local Solvability of D(theta).

Abstract:

:Let E and F be vector bundles and D:E --> F an operator of order k. We associate a sequence of invariants ((l))(D), l >/= 0 with D which generalize the concept of curvature in a natural way. In the case where D = D(theta) is the differential operator of a connection theta on a vector bundle E, ((1))(D(theta)) is the classical curvature. Furthermore, we find an interesting geometric interpretation for ((2))(D(theta)). Finally, given regularity assumptions, we find, with the aid of these invariants, necessary and sufficient conditions for local solvability of D(theta).

authors

Knapp RE

doi

10.1073/pnas.70.3.797

subject

Has Abstract

pub_date

1973-03-01 00:00:00

pages

797-8

issue

3

eissn

0027-8424

issn

1091-6490

journal_volume

70

pub_type

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