Necessary conditions for a superdifferentiable supercurve to be a weak minimum relative to two sub-supermanifolds. (English) Zbl 1039.58006

Cristea, Valentin

Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 4th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 6–15, 2002. Sofia: Coral Press Scientific Publishing (ISBN 954-90618-4-1/pbk). 161-167 (2003).

The author gathers some general definitions and several of his previous results in order to present the frame of reference for the statement and proof of some necessary conditions (in terms related to the Legendre supertransformation) for a piecewise superdifferentiable supercurve (in the sense of A. Rogers) to be a weak local minimum relative to two sub-supermanifolds.
For the entire collection see [Zbl 1008.00022].

Reviewer: Eugen Pascu (Montreal)

MSC:

58A50	Supermanifolds and graded manifolds
58E99	Variational problems in infinite-dimensional spaces
58E50	Applications of variational problems in infinite-dimensional spaces to the sciences

Keywords:

differentiable supermanifold; Legendre supertransformation; regular problem in the calculus of variations; supercurve; sub-supermanifold