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.
Original language | English |
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Pages (from-to) | 25-42 |
Number of pages | 18 |
Journal | Journal of Geometry and Physics |
Volume | 14 |
Issue number | 1 |
Publication status | Published - Jun 1994 |
Keywords
- HARMONIC SECTION
- GRASSMANN BUNDLE
- ALMOST-PRODUCT STRUCTURE
- TOTALLY GEODESIC
- NIJENHUIS TENSOR
- WEITZENBOCK FORMULA
- CODAZZI EQUATION
- BIANCHI IDENTITY
- RIEMANNIAN FOLIATION