Croke, C.; Fathi, A. An inequality between energy and intersection. (English) Zbl 0719.53020 Bull. Lond. Math. Soc. 22, No. 5, 489-494 (1990). By introducing a quantity called intersection of metrics g, \(g'\) under a continuous map f: (M,g)\(\to (N,g')\) between Riemannian manifolds, the authors establish an inequality between the energy of f and intersection. They prove that the identity map on a closed Riemannian manifold without conjugate points is energy minimizing in its homotopy class. Reviewer: H.Özekes (İstanbul) Cited in 2 ReviewsCited in 14 Documents MSC: 53C20 Global Riemannian geometry, including pinching Keywords:intersection of metrics; continuous map; inequality; energy minimizing PDFBibTeX XMLCite \textit{C. Croke} and \textit{A. Fathi}, Bull. Lond. Math. Soc. 22, No. 5, 489--494 (1990; Zbl 0719.53020) Full Text: DOI