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).
journal_name
Proc Natl Acad Sci U S Aauthors
Knapp REdoi
10.1073/pnas.70.3.797subject
Has Abstractpub_date
1973-03-01 00:00:00pages
797-8issue
3eissn
0027-8424issn
1091-6490journal_volume
70pub_type
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