Conformal Geometry, Contact Geometry, and the Calculus of Variations

  title={Conformal Geometry, Contact Geometry, and the Calculus of Variations},
  author={JEFF A. VIACLOVSKY},
  • Published 1999
for metricsg in the conformal class of g0, where we use the metric g to view the tensor as an endomorphism of the tangent bundle and where σk d notes the trace of the induced map on the kth exterior power; that is, σk is the kth elementary symmetric function of the eigenvalues. The case k = 1,R = constant is known as the Yamabe problem, and it has been studied in great depth (see [11] and [17]). We let M1 denote the set of unit volume metrics in the conformal class [g0]. We show that these… CONTINUE READING
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