TL;DR
This paper introduces new field-theoretic constructions for multiple integrals, generalizing classical transforms and exploring geometric properties of bundles related to extremals.
Contribution
It presents novel generalizations of the Legendre-Weyl-Caratheodory transforms and investigates the connection and curvature of bundles induced by extremal fields.
Findings
Generalized transforms for multiple integrals introduced.
Connection and curvature of extremal bundles calculated.
New invariant integrals developed.
Abstract
New constructions in the theory of fields for multiple integrals are designed. Generalizations of the Legendre - Weyl - Caratheodory transforms and corresponding invariant integrals are introduced and explored. Connection and curvature of bundles induced by a field of extremals are calculated.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Stochastic processes and financial applications · Advanced Mathematical Modeling in Engineering