The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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NIJENHUIS TENSOR FUNCTIONAL ON A SUBSPACE OF METRICS

  • Kang, Bong-Koo (Department of Computer Science Sanju National Polytechnic University)
  • Published : 1994.12.01
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Abstract

The study of the integral of the scalar curvature, $A(g)\;=\;{\int}_M\;RdV_9$ as a functional on the set M of all Riemannian metrics of the same total volume on a compact orient able manifold M is now classical, dating back to Hilbert [6] (see also Nagano [8]). Riemannian metric g is a critical point of A(g) if and only if g is an Einstein metric.(omitted)

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