  A theory of the upper critical field in a trigonal superconductor with a
two-component order-parameter is developed. We demonstrate the existence of
sixfold modulations of the upper critical field in the basal plane. The form of
the angular dependence of H_c2 in the plane of the main symmetry axis is
studied in the whole range of phenomenological rigidity coefficients. A
qualitative dependence of these coefficients on the form of the Fermi surface
is established. The results obtained are discussed in connection with the
measurements of the direction dependence of H_c2 in the heavy fermion
superconductor UPt_3 that has been recently found to possess trigonal
crystalline structure.
  PACS numbers: 74.20.De, 74.70.Tx
