A CLASS OF HARMONIC ALMOST-PRODUCT STRUCTURES

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JournalJournal of Geometry and Physics
DatePublished - Jun 1994
Issue number1
Volume14
Number of pages18
Pages (from-to)25-42
Original languageEnglish

Abstract

The energy of a Riemannian almost-product structure P is measured by forming the Dirichlet integral of the associated Gauss section gamma, and P is decreed harmonic if gamma criticalizes the energy functional when restricted to the submanifold of sections of the Grassmann bundle. Euler-Lagrange equations are obtained, and geometrically transformed in the special case when P is totally geodesic. These are seen to generalize the Yang-Mills equations, and generalizations of the self-duality and anti-self-duality conditions are suggested. Several applications are then described. In particular, it is considered whether integrability of P is a necessary condition for gamma to be harmonic.

    Research areas

  • HARMONIC SECTION, GRASSMANN BUNDLE, ALMOST-PRODUCT STRUCTURE, TOTALLY GEODESIC, NIJENHUIS TENSOR, WEITZENBOCK FORMULA, CODAZZI EQUATION, BIANCHI IDENTITY, RIEMANNIAN FOLIATION

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